WO2023282782A1

WO2023282782A1 - Amplitude and phase modulator based on semiconductor lasers

Info

Publication number: WO2023282782A1
Application number: PCT/RU2021/000291
Authority: WO
Inventors: Роман Алексеевич ШАХОВОЙ; Александр Валерьевич ДУПЛИНСКИЙ; Виолетта Владимировна ШАРОГЛАЗОВА; Арина Альбертовна ГАВРИЛОВИЧ; Денис Васильевич СЫЧ; Антон Вадимович ЛОСЕВ; Владимир Владимирович Заводиленко; Юрий Владимирович КУРОЧКИН; Марюс ПУПЛАУСКИС
Original assignee: Общество С Ограниченной Ответственностью "Курэйт"
Priority date: 2021-07-09
Filing date: 2021-07-09
Publication date: 2023-01-12

Abstract

The present technical solution relates in general to the field of quantum cryptography, and more particularly to phase modulators and amplitude and phase modulators operating on the basis of optical injection into semiconductor lasers for quantum key distribution. The technical result achieved by the present solution consists in providing for quantum key distribution. In a first preferred embodiment, an amplitude and phase modulation device for quantum key distribution is proposed, which is designed to be capable of creating quantum states in a phase basis and a time basis, said device comprising: a slave laser capable of generating optical data pulses suitable for creating quantum states; a master laser capable of setting a phase basis and a time basis with the aid of optical pulses of different lengths, wherein state encoding in the phase basis is carried out by disturbing the pumping current in the middle of a long pulse, and state encoding in the time basis is carried out by selection of the generation time of a short pulse; and an optical circulator capable of transmitting radiation from the master laser to the slave laser and coupling the radiation of the slave laser into an optical attenuator.

Description

AMPLITUDE-PHASE MODULATOR ON SEMICONDUCTOR LASERS

TECHNICAL FIELD [0001] This technical solution relates to the field of quantum cryptography, and more specifically to phase and amplitude-phase modulators based on the use of optical injection in semiconductor lasers for quantum key distribution.

BACKGROUND OF THE INVENTION [0002] Optical radiation modulation is the technological basis for data transmission in telecommunications. In most cases, amplitude and phase modulation (keying) of laser radiation is carried out using modulators based on LiNbCb, which have been the "workhorse" in the field of optoelectronics for decades. Despite the popularity and high efficiency of modulators of this type, they have a number of disadvantages that become more and more noticeable with the continuous development of fiber optic systems, in particular, in connection with the development of quantum key distribution (QKD) methods.

[0003] Although LiNbCb-based broadband modulators have been mass-produced for a long time, high-speed devices still have a high cost: the price of some models can be several times higher than the cost of standard telecommunication lasers and fiber optic elements. Therefore, the research and development of an efficient and at the same time cheaper modulation method is highly expedient from an economic point of view. Other important factors are: 1) the relatively large size of LiNbCb-based phase modulators, whose characteristic lengths usually reach several centimeters, and 2) the high half-wave voltage. These features limit their use in photonic integrated circuits (PIC) compatible with CMOS (complementary metal-oxide-semiconductor) technology.

[0004] One of the most common methods of modulating an optical signal is phase modulation (or phase shift keying, if the information signal is discrete), in which the measured parameter is the phase of the optical signal or the phase difference between adjacent optical signals (in the latter case, they speak of differential phase shift keying ). Phase coding is of particular importance today in connection with the development of QKD systems, where cryptographic keys are usually encoded in the phase of attenuated laser pulses

[1]. Following the global trend towards miniaturization and development of FIS, system developers

QRCs are looking for efficient transmitters (modulators) on a chip. As a rule, high requirements are imposed on such transmitters, including not only compactness, low losses and compatibility with CMOS technologies, but also the absence of undesirable effects leading to information leakage through side channels. Recently, Yuan et al. [2] have demonstrated a direct phase modulation scheme that appears to meet these requirements and is thus one of the possible candidates to replace (at least in some applications) LiNbCb based phase modulators.

[0005] The direct phase modulation scheme proposed by Yuan et al. is based on the known phenomenon of phase locking in an optically injected laser [3, 4]. It uses two semiconductor lasers, one of which (the pulse preparation laser) operates in the gain-switched mode, and the second (the phase preparation laser) operates in a quasi-stationary regime, with small perturbations of the master pump current used to control the phase between adjacent pulses of the slave laser. laser. Recently, this scheme has been successfully implemented in QKD systems [5, 6]. It should be noted that, despite the well developed theory of semiconductor lasers with optical injection, a detailed model of direct phase modulation by means of optical injection appeared in the literature quite recently [7].

[0006] Another common method for modulating an optical signal is amplitude modulation, in which the measured parameter is light intensity. The most direct method of amplitude modulation of laser radiation is to change the pump current of a semiconductor laser, i.e. so-called direct amplitude modulation. This method is extremely convenient, since the output optical power of a semiconductor laser in a wide range of values is proportional to the injection current, so that the conversion of an electrical signal into an optical one is linear, so no additional equipment is required to create a digital optical signal. In addition, the lifetime of carriers in the active layer of a semiconductor laser is quite short (~1 ns), and since the lifetime of photons in the resonator is about three orders of magnitude shorter, the frequency of direct amplitude modulation in semiconductor lasers can reach several tens of gigahertz. However, the transmission of such optical signals is a very difficult task, since short laser pulses obtained by direct amplitude modulation are characterized by significant frequency modulation (chirp), which leads to a significant broadening of the pulse when propagating along the optical fiber even over small (several kilometers) distances and, as a result, to the impossibility of extracting the information encoded in them. For this reason, at a data rate of more than 1 Gbit / s, a semiconductor laser, as a rule, operates in a continuous mode, and an external amplitude modulator (usually again based on LiNbCb) is used to obtain an optical digital signal.

[0007] In the context of the foregoing, a logical question arises: is it possible to use the above-mentioned optical injection scheme not only for phase, but also for amplitude modulation? In other words: is it possible to create a compact, FIS-compatible, and suitable for use in QKD systems, an amplitude-phase modulator? To the authors' knowledge, there is no description of such a device in the literature. In this paper, the authors intend to demonstrate the implementation of such a device, briefly outline its mathematical model (give a theoretical justification for its operation), and describe how it can be used as a QKD transmitter.

SUMMARY OF THE INVENTION

[0008] The claimed invention is directed to solving a technical problem inherent in known prior art approaches.

[0009] The technical result is to create a more miniature single optical system that provides amplitude-phase modulation for encoding information.

[0010] Another technical result is to increase the efficiency of transmission of quantum states of photons due to amplitude-phase modulation.

[0011] The claimed technical result is achieved through an amplitude-phase modulation device for quantum key distribution, made with the ability to create quantum states in phase and time bases, containing:

- a controlled laser configured to generate information optical pulses suitable for creating quantum states;

- a control laser configured to set the phase and time bases using optical pulses of different durations, wherein the state encoding in the phase basis is carried out using a perturbation of the pump current in the middle of a long pulse, and the state encoding in the time basis is carried out by selecting the short pulse generation time; - an optical circulator configured to transmit radiation from the control laser to the controlled laser and output the radiation of the controlled laser to the optical attenuator.

[0012] In one of the particular examples of implementation, the output of the controlled laser additionally contains an intensity modulator designed to equalize the amplitude of the states in time and phase basis.

[0013] In another particular implementation, the long pulses are unperturbed rectangular pulses and rectangular pulses with a pump current perturbation in the middle.

[0014] In another particular implementation, the long pulse from the control laser is shifted in time so that it starts earlier than the pulse of the controlled laser.

[0015] In another particular embodiment, the device further comprises an optical bandpass filter.

[0016] In another particular embodiment, the optical band pass filter is at least a passive fiber optic DWDM filter. [0017] In yet another particular embodiment, the transmission frequency of the optical band-pass filter is chosen so that all the radiation of the controlled laser in the absence of optical injection is completely absorbed.

[0018] In another particular embodiment, the device further comprises an unbalanced interferometer.

[0019] In another particular embodiment, the device further comprises two unbalanced interferometers.

[0020] In another particular embodiment, the steerable and control lasers are at least semiconductor lasers coupled by optical injection.

[0021] The claimed technical results are also achieved by a quantum key distribution (QKD) system containing an amplitude-phase modulation device for quantum key distribution, connected via a quantum communication channel to a receiving device, wherein:

- the amplitude-phase modulation device for quantum key distribution further comprises: o an optical attenuator configured to attenuate the signal before it is transmitted to the quantum channel; o a controller configured to control laser drivers that set electrical pulse sequences to the control and slave lasers;

- the receiving device is configured to distinguish between the phase and time bases by selecting a slot within the time window allocated for one quantum state and decoding the states in the specified bases, while the receiving device contains: the corresponding delay time was a multiple of the repetition period of the information pulses generated by the controlled laser; o a broadband phase modulator that allows you to change the phase in one of the arms of the interferometer in a controlled manner and select states in the phase basis; o at least one single photon detector configured to operate in a gating mode, which is necessary for selecting a basis; o a receiver controller configured to control a broadband phase modulator in the interferometer arm and single photon detectors.

[0022] In one particular embodiment, the time window (frame) allocated for a quantum state contains at least three time slots.

[0023] In another particular embodiment, the selection of the basis by the receiving device is carried out by at least sending a strobe pulse to at least one single photon detector in a certain time slot of the quantum state time window.

BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings, which are included in this description to provide additional understanding of the essence of the claimed solution and form part of it, illustrate options for implementation and together with the description serve to explain the principles of implementation and operation of the claimed solution.

On the drawings:

Numerical designations: 1 - control laser (master), 2 - controlled (slave) laser, 3 - optical isolator, 4 - beam splitter, 5 - optical terminator, 6 - optical circulator, 7 - bandpass optical filter, 8 - tunable optical attenuator, 9 - quantum channel, 10 - broadband (high-frequency) phase modulator, 11, 12 - single photon detectors, 13 - Alice transmitter, 14 - receiver

Bob, 15 - photodetector, 16 - narrow-band (low-frequency) phase modulator, 17 - amplitude modulator.

[0025] In FIG. Error! The source of the reference was not found, the schemes of optical injection "for transmission" (a) and "for reflection" (b, c) are shown.

[0026] In FIG. Error! Reference source not found, implementation of amplitude-phase modulator (Alice's transmitter) and demodulator (Bob's receiver) corresponding to Scheme I is shown.

[0027] In FIG. Error! Reference source not found, computer simulations of laser pulse sequences are shown that implement the method of preparing quantum states in Scheme I.

[0028] In FIG. Error! Reference source not found, implementation of amplitude-phase modulator (Alice's transmitter) and demodulator (Bob's receiver) corresponding to Scheme II is shown.

[0029] In FIG. Error! Reference source not found, computer simulations of laser pulse sequences are shown that implement the method of preparing quantum states in Scheme I.

[0030] In FIG. Error! Reference source not found, computer simulations of laser and electrical control pulse sequences are shown explaining how to ensure that the pulses in circuit II are indistinguishable.

[0031] In FIG. Error! Reference source not found, implementation of amplitude-phase modulator (Alice's transmitter) and demodulator (Bob's receiver) corresponding to Scheme III is shown.

[0032] In FIG. Error! Reference source not found, computer simulations of laser pulse sequences are shown that implement the method of preparing quantum states in Scheme III.

[0033] In FIG. Error! Reference source not found shows an implementation of an amplitude-phase modulator (Alice's transmitter) and a demodulator (Bob's receiver) corresponding to Scheme IV.

[0034] In FIG. Error! Reference source not found, computer simulations of laser pulse sequences are shown that implement the method of preparing quantum states in Scheme IV. [0035] In FIG. Error! Reference source not found, Bloch spheres are shown, on which quantum states C _ϋ , and Z _oi are marked with dots, prepared in Schemes I—III.

[0036] In FIG. Error! The reference source was not found, the implementation of the amplitude-phase modulator (Alice's transmitter) and the demodulator (Bob's receiver) is shown, corresponding to Scheme I with an amplitude modulator to equalize the amplitudes of the states in different bases.

[0037] In FIG. Error! Reference source not found, computer simulations of laser pulse sequences are shown that implement the method of preparing quantum states in Scheme I with an amplitude modulator.

[0038] In FIG. Error! The reference source was not found, the implementation of the amplitude-phase modulator (Alice's transmitter) and the demodulator (Bob's receiver) is shown, corresponding to Scheme II with an amplitude modulator to equalize the amplitudes of the states in different bases.

[0039] In FIG. Error! The reference source was not found, the implementation of the amplitude-phase modulator (Alice's transmitter) and the demodulator (Bob's receiver) is shown, corresponding to Scheme III with an amplitude modulator to equalize the amplitudes of the states in different bases.

[0040] In FIG. 16 shows a general view of the computing system.

IMPLEMENTATION OF THE INVENTION

[0041] Quantum key distribution

[0042] Quantum Key Distribution (QKD) is a cryptographic key transmission (distribution) method that uses quantum phenomena to guarantee communication privacy. In QKD, as in classical cryptographic schemes, the device that transmits secret information is called Alice, and the device that receives this information is called Bob. A third party who tries to gain unauthorized access to the transmitted information is called Eve (from the English “eavesdropper” - eavesdropper). To date, QKD is one of the most mature quantum technologies that marked the so-called second quantum revolution [8].

[0043] By definition, QKD uses individual quanta, usually photons, to transmit the key. Each quantum of light can be used as a carrier of a unit of quantum information - a qubit. In this case, the photon is considered as a two-level system, where the states are chosen as orthogonal states polarization. In practical applications, however, single photons are rarely used, since the currently available sources of single photons have an extremely low efficiency. Therefore, most often in QKD, strongly attenuated laser pulses are used as qubits, which are not single photons, but coherent states with an average photon number much less than unity.

[0044] To date, quite a few different CRK protocols have been described in the literature, but the protocol proposed by C. Bennett and J. Brassard in 1984, the so-called BB84 protocol [9], is the most commonly used. In this protocol, Alice prepares quantum states in two non-orthogonal bases: if the polarization states of a photon are used, then vertical-horizontal and diagonal-antidiagonal bases can be chosen as such bases (we can conventionally call them X-basis and Y-basis, respectively). The photon polarization vector in the X-basis is directed horizontally <-> or vertically X , and the <-» state can be assigned 0, and the state - 1. In the Y-basis, polarization states can be used

moreover, the state can be assigned 0, and the state - 1. To prepare quantum states, Alice uses a random number generator, i.e. the choice of the basis and a specific state in the basis is carried out randomly. The prepared quantum states (attenuated laser pulses with a given direction of the electric field polarization vector) are sent to Bob through the quantum channel. (For definiteness, we will assume that a fiber optic line acts as a quantum channel, although the atmosphere, for example, in a satellite QKD, or even water can be used for quantum key transmission.) Bob measures the quantum states transmitted to him, also choosing a basis randomly. The measurement results are recorded, and then, via an open channel, Bob tells Alice which photons he managed to measure and which bases he chose (the result of the measurements is not disclosed); Alice reports back in which dimensions the bases were chosen correctly. Measurement results corresponding to incorrectly chosen bases are discarded, and the remaining measurement results are the so-called sifted key. The sifted key is then subjected to error correction and security enhancement procedures, after which Alice and Bob have an identical sequence of bits at their disposal, which can already be used for cryptographic purposes.

[0045] If Eve intervenes in a key transfer session, then her presence is easily detected due to the quantum nature of the transmitted states, more precisely, thanks to the so-called no-cloning theorem [10]. According to this theorem, a separate quantum state cannot be copied (cloned), since this contradicts the mathematical apparatus of quantum mechanics, namely, it contradicts the linearity of the Hilbert space. Thus, Eve will not be able to copy the qubits

Alice in order to send them in an unchanged state to Bob and later, listening to Alice's and Bob's messages over an open channel, restore the transmitted key. In other words, Eve is forced, like Bob, to measure quantum states and only then transfer them to him. However, since Alice does not use orthogonal bases, but

Eve is forced to choose measurement bases randomly (after all, she does not have access to Alice's random number generator), then she will inevitably introduce an error into the transmitted qubits. Thus, estimating the number of errors in the transmitted key,

Alice and Bob will be able to notice Eve's presence and realize that their key has been compromised.

[0046] It should be noted that if Alice uses weakened coherent states instead of single photons, then Eve has an additional opportunity to eavesdrop on the key without being noticed. It can carry out the so-called attack on the division of the number of photons [11, 12]. To counteract this attack, a technique of decoy states [13, 14] was developed — additional coherent states that Alice sends to Bob mixed with information states, and in which the average number of photons differs from the average number of photons in information pulses. Since Eve does not know which impulses are informational, she will act on all impulses. By then disclosing information about which of the pulses were decoys, Alice and Bob will be able to understand whether the attack was carried out by dividing the number of photons, i.e. will be able to notice the presence of Eve.

Since decoy states in essence do not change the BB84 protocol itself, but are only an add-on to it, below for brevity we will consider a “pure implementation” of this protocol, implying (or stipulating where necessary) that each of the implementations considered below can be implemented also with bait states.

[0047] To implement polarization coding in the BB84 protocol, it is not necessary to use horizontal-vertical (canonical) and diagonal-antidiagonal bases. From an experimental point of view, it is more convenient to use, for example, diagonal-antidiagonal and circular bases as non-orthogonal bases [15]; in the latter one can use right-circular T and left-circular Y polarizations of light as orthogonal states. When using these two (non-orthogonal) bases, the choice of state can be carry out using a phase modulator, which can be configured in such a way that when a laser pulse with a known direction of the polarization vector passes through it, a given phase shift of the orthogonally polarized components occurs; By controlling this phase delay, one can change the polarization states by choosing from the set: , T and U .

[0048] Instead of polarization states, the phase of a coherent state (photon) can also be used for encoding. Generally speaking, from a mathematical point of view, phase and polarization coding are equivalent. The implementations of both types of encoding are also similar: in both cases, a phase modulator is used to prepare the states. In phase coding, coherent states with phases 0 and p can be used as the X-basis, and states with phases n/2 and 33/2 as the U-basis.

[0049] It should be noted that when phase-coding individual coherent states, the optical scheme can be assembled in such a way that it will be insensitive to changes in the polarization of the radiation in the pulse, due to polarization-mode dispersion [1]. However, during phase encoding, it is necessary to ensure temperature stabilization of the interferometers on the side of Alice and Bob, which are usually used to decode transmitted qubits. With polarization coding, there is no need to use interferometers and, accordingly, there is no need to provide temperature stabilization of the optical scheme. In polarization encoding, however, one has to use polarization controllers to compensate for the polarization-mode dispersion in the quantum channel. Thus, implementations of both types of encoding have their own advantages and disadvantages.

[0050] As stated in the prior art, the use of LiNbCb based phase modulators can be considered (in a certain context) as a shortcoming in the implementation of the QKD system, which can be circumvented by using an (amplitude-)phase modulator on optical injection. This phase modulation method, however, is not suitable for polarization coding; as will be shown below, it is most convenient for differential phase coding, in which information is encoded not in the phase of an individual coherent state, but in the phase difference between adjacent pulses. In the future, we will consider this particular method of phase coding for QKD.

[0051] Finally, in addition to phase and / or polarization coding, so-called temporal coding is also used, in which information encode the time of arrival of the laser pulse at the photodetector, more precisely, the response time of the detector of single photons. Here, as in the case of differential phase coding, not one coherent state, but a pair of pulses is used to transmit a qubit. If the first pulse in a pair is "empty" (vacuum state), then such a pair can be assigned the value 1, if the second pulse is "empty", then the value 0 is assigned to it. Usually, the basis used for time coding is denoted by the letter Z. As a non-orthogonal basis, one can use, for example, the X-basis of differential phase coding.

[0052] Optical injection schemes

[0053] In edge-emitting semiconductor lasers (traditional Fabry-Perot lasers, as well as single-frequency distributed feedback or distributed Bragg reflector lasers), optical injection is typically performed by one of the methods shown in FIG. Error! Reference source not found. FIG. Error! Reference source not found. (a) shows the so-called “transmission” scheme, when the radiation from the control laser (1) enters the controlled laser (2) from one end, and the output radiation is recorded from the opposite end. To prevent unwanted feedback, i.e. radiation from the slave laser back to the master, in this scheme, an optical isolator (3) is installed at the output of the control laser. The scheme in Fig. Error! Reference source not found. (a) is preferred in photonic integrated circuits (PICs) because it is the most compact and simple.

[0054] An alternative optical injection scheme is the so-called "reflective" scheme. One of its implementation options is shown in Fig. Error! Reference source not found. (b), where radiation from the master is fed into the controlled laser through one of the input ports of the beam splitter (4), and output from the controlled laser through the second port. On FIG. Error! Reference source not found. (b) shows that the unused output port of the beam splitter is terminated, i. an optical terminator (5) is installed at its end. The main purpose of the terminator here is to prevent "contamination" of the output radiation by unwanted reflections from the end of the waveguide. Note, however, that the use of a terminator is generally not mandatory, and the mentioned reflections are often simply neglected.

[0055] Finally, in FIG. Error! The reference source was not found. (c) shows the scheme of optical injection "on reflection" using an optical circulator (6). The optical circulator transmits radiation from the master to the slave laser, and outputs the radiation of the latter to a separate port, and the master automatically turns out to be isolated from the radiation of the controlled laser. Such a circuit is in most cases more preferable than the circuit shown in FIG. Error! The reference source was not found. (b) because the circulator passes almost all the power of the master, while in the circuit of FIG. Error! Reference source not found. (b) Part of the master's radiation is cut off by the beam splitter. It should be noted that the "reflective" circuits are more convenient in fiber design, and also allow the use of standard telecommunication laser modules, which do not provide a second port for the output of laser radiation.

[0056] All three circuits shown in FIG. Error! The source of the link was not found., are equivalent to one degree or another, therefore, without detracting from the generality of the presentation, we will continue to use the scheme with an optical circulator in all drawings (Fig. Error! The source of the link was not found. (c)), implying, however, , that instead of it can (and in the context of the FIS - should) be used the “transmission” circuit (Fig. Error! Reference source not found. (a)), or a scheme with a beam splitter (Fig. Error! Reference source not found. ( b)).

[0057] Mathematical model

[0058] In most cases, to adequately describe the dynamics of semiconductor lasers in the presence of optical injection, it is sufficient to use the approximation of rate equations. If the pumping of the control and controlled lasers is a function of time (and for amplitude-phase modulation, this is the case that should be considered), then the dynamics of laser generation is described by a system of 6 nonlinear differential equations, three of which describe the time dependence of the normalized intensity (number of photons) Q ^M , number of carriers N ^M and phase f ^M of the master:

and the other three determine the dynamics of the number of photons Q, the number of carriers N, and the phase f of the slave laser:

[0059] In equations (1) and (2), the superscript M indicates the values corresponding to the master. The gain G is here defined as a dimensionless normalized quantity as follows: G

, where N _tr is the number of carriers at which the active layer material is transparent at the wavelength of the considered laser mode, and N _th is the threshold number of carriers. Further, _te and are the lifetimes of carriers and photons, respectively; Г - mode confinement coefficient (confinement factor); C _sp is the average fraction of spontaneously emitted photons falling into the considered laser mode; a is the line broadening coefficient (the so-called Henry factor); I - pump current; e is the absolute value of the electron charge; k _ίh] is the coupling coefficient between the control and slave lasers, which determines the efficiency of optical injection; D oo _inj - detuning of lasers in frequency and, finally,

F _n , F _Q and F are random Langevin forces responsible for fluctuations in the number of carriers, the number of photons, and the phase, respectively. In explicit form, the Langevin forces are written as follows (in the form of differentials):

where W ^A , W ^B and W ^c are independent Wiener processes. It should be noted that for the master in equations (3) each value must be assigned the index M ; in addition, three other independent Wiener processes must be introduced for it (thus, there must be 6 of them in total).

[0060] Implementation of an amplitude-phase modulator. Scheme I

[0061] One possible implementation of an amplitude-phase modulation transmitter and its corresponding receiver is shown in FIG. Error! Reference source not found. Under the transmitter or transmitting device in this solution, we will understand the amplitude-phase modulation device for quantum key distribution. To avoid confusion in the future, this implementation of the transmitter (amplitude-phase modulation device for quantum key distribution) will be conventionally called Scheme I. From FIG. Error! Reference source not found. It can be seen that this circuit is similar to the circuit shown in Fig. Error! The source of the link was not found. (c), however, there are differences in it, consisting in the addition of an optical band-pass filter (7), the purpose of which we will discuss below, and a tunable optical attenuator (8), which is used to attenuate laser pulses, i.e. to create weak coherent states suitable for use in quantum key distribution (QKD) protocols. In this scheme, the controlled laser (2) acts as a generator of information optical pulses, and the control laser (1) sets the phase and amplitude modulation of the resulting pulse sequence.

[0062] An example of an optical pulse train leaving the master and the corresponding slave laser pulse train (before they pass through the optical band pass filter) are shown in FIG. Error! Reference source not found.(a). To simulate optical signals, systems of equations (1) and (2) were used (Langevin noise was not taken into account in this example); in the simulations, the pulse repetition rate of the controlled laser is 1.25 GHz, and the bias currents on both lasers were set below the threshold value, i.e., both lasers were assumed to operate in the gain switching mode. From FIG. Error! The reference source was not found. (a) it can be seen that the master generates three types of laser pulses: short ones, the duration of which is approximately equal to the period T _p of the slave laser pulses, as well as long pulses with a duration approximately equal to 2T _p . Long pulses are used to encode the phase between adjacent controlled laser pulses, while short pulses are used to implement amplitude shift keying.

[0063] Consider first the phase encoding. From FIG. Error! The source of the link was not found. (a) it can be seen that in this scheme two types of long pulses are used: one of them is a regular rectangular pulse, while the other has a small disturbance in the middle - a “pit”. First of all, we note that the long pulse from the master is deliberately shifted in time so that it starts earlier than the slave laser pulse, so that the relaxation processes on the master have time to end before the generation of the information pulse begins, so we can assume that during the time when a pair of pulses of the slave laser is generated, the master shines in a stationary mode. In this case, a small perturbation of the pump current, which makes it possible to create a "pit" in the middle of a long laser pulse, does not lead to significant relaxation oscillations on the master, so we can assume that at the bottom

“pits” the radiation of the master is also stationary (although it differs in output power and frequency), so we will call this generation mode quasi-stationary.

[0064] If there were no radiation from the master, then two adjacent slave laser pulses would be emitted with completely random initial phases [16], since, as indicated above, we assume that the lasers operate in a gain switching mode. If the slave laser pulses are generated during the time when the master emits a long pulse, then between adjacent pulses of the controlled laser, its resonator “does not empty”. Indeed, it now contains control laser radiation, which will initiate laser generation during the next pulse. Thus, the phase difference between a pair of slave laser pulses emitted during the time when the master is shining will no longer be random, but will be determined by the evolution of the electric field in the master pulse, i.e. will depend on the frequency of the control laser radiation. It is well known that the lasing frequency strongly depends on the carrier concentration in the active layer, which is associated with the dependence of the refractive index of a semiconductor material on the number of electrons and holes. Thus, when the pump current changes, not only its output power, but also the generation frequency will change in the laser. Therefore, in a semiconductor laser, it is possible to control the frequency of the electric field in a pulse using the pump current. The phase difference between the slave laser pulses emitted during the time that the master emits a long pulse will depend on whether a "pit" was present in the pulse or not. The depth of the "pit" can be chosen such that the phase difference between the corresponding pulses of the slave laser was, for example, a multiple of p, and the phase difference between the pulses emitted together with the long pulse of the master without the "pit" was a multiple of 2g. In this case, one can easily distinguish between the signals encoded by the master's pulses with and without a "pit" by combining the corresponding pairs of information pulses in an interferometer (for example, in a Mach interferometer).

Zehnder or Michelson), the length of the delay line AL of which is chosen so that the delay time is exactly equal to the period of the information pulses.

It is this decoding method that is assumed on the receiver side.

(receiving device) (14) in FIG. Error! Reference source not found., which shows a Mach-Zehnder interferometer having an appropriate delay line AL and equipped with a phase modulator (10). We will look at the decoding method in more detail below. [0065] With regard to amplitude modulation, in Scheme I, it is carried out using frequency filtering. At the output of the slave laser, an optical band pass filter (7) is installed (for example, a standard passive fiber optic DWDM (Dense Wavelength Division Multiplexing) filter), the transmission frequency of which is chosen so that all radiation from the slave laser (in the absence of optical injection) is completely in it was absorbed. Thus, in order to suppress the pulse of the controlled laser, which should not fall into the quantum channel, it is sufficient to turn off the control laser at the time corresponding to this pulse. And vice versa, in order for the band-pass filter to pass the necessary information pulses, it is necessary to turn on the master for each such pulse (or pair of pulses). This effect occurs due to the phenomenon of phase synchronization, which lies in the fact that the frequency of the electric field in the controlled laser pulses that appear in the presence of radiation from the master is generated at the frequency of the control laser field (with a correctly selected detuning Aco _inj ). Therefore, by shifting the master frequency to the optical filter passband (7), we obtain effective amplitude modulation: only those slave laser pulses, the generation of which is accompanied by the generation of the master, will enter the quantum channel.

[0066] The sequence of "filtered" information pulses corresponding to the signal from the master in FIG. Error! Reference source not found. (a), shown in FIG. Error! Reference source not found.(b). It can be seen that pairs of information pulses correspond to long pulses of the control laser, and single pulses correspond to short pulses of the master. In addition, from FIG. Error! The source of the link was not found. (a) it can be seen that in the sequence of pulses of the controlled laser there are "silent" or separating pulses, which, as we will see below, are necessary for correct decoding. Due to frequency filtering, however, these pulses do not enter the quantum channel, as can be seen from FIG. Error! Reference source not found.(b).

[0067] From the point of view of quantum key distribution (QKD), the choice of long or short pulses on the master corresponds to the choice of basis: long pulses correspond to the choice of "phase basis" X , and short pulses correspond to the choice of "time basis" Z . Bit encoding in the X-basis is carried out using a pump current perturbation in the middle of the pulse: 1 is encoded by the absence of a “pit”, and 0 is encoded by its presence. Bit encoding in the Z-basis is carried out by choosing the generation time of a short pulse on the master: separating pulse, then 0 is encoded, if after the separating pulse of the controlled laser follows another "silent" pulse, then encoded 1. For clarity, in FIG. Error!

Reference source not found. (b) Rectangles encircle pulses that encode a bit in one or another basis.

[0068] Thus, based on the above, in one particular embodiment for quantum key distribution, the transmission of photon quantum states can be implemented by an amplitude-phase modulation device, which is disclosed in this description as Scheme I. As mentioned above, this device is configured to creation of quantum states in phase and time bases, using at least controllable and controlling lasers, and an optical circulator. For a person skilled in the art, it will be obvious that further disclosure of the features of the present technical solution can also be implemented using the specified device with appropriate modifications.

[0069] As mentioned above, the decoding of the received pulse sequence is carried out using the receiving device. In one particular embodiment, such a device can be, for example, an unbalanced Mach-Zehnder or Michelson interferometer (in Fig. Error! Reference source not found, Bob's receiver (14) shows a Mach-Zehnder interferometer), the length of the delay line DZ of which is chosen such as to receive the interference of adjacent pulses. The corresponding interference result is shown in FIG. Error! Reference source not found.(c). It can be seen that the resulting sequence of pulses can be divided into separate time windows (frames), divided into three time slots

, t ₂ and t ₃ . After such a division, it becomes clear why separating pulses are needed: they are necessary so that the information pulses corresponding to different bases do not overlap at the exit from the interferometer, but always belong to separate frames.

[0070] The choice of the basis on the side of Bob is carried out by choosing a time slot within the frame, which can be done, for example, by sending a strobe pulse to the single photon detectors (11, 12) at time points

, t ₂ or t ₃ . From FIG. Error! Reference source not found. (c) it can be seen that if the strobe coincides with the time slot t ₂ , then this corresponds to Bob's choice of the X-basis. In this case, if detector 11 (destructive interference) is triggered, then bit 0 will be unambiguously decoded; if detector 12 (constructive interference) is clicked, then bit 1 will be decoded. (Here it is assumed that the phase modulator (10) in the receiver Boba was pre-configured so that the phase difference between the information pulses, coded by Alice using long pulses without a "pit" corresponded to constructive interference.) If the strobe pulse coincides with the time slot or t ₃ , then this corresponds to Bob's choice of the Z-basis. For definiteness, we will assume that the Z -basis is always chosen in the time slot t ₃ . In this case, if at least one of the detectors clicks, then Bob uniquely decodes 1. It is important to note that zero decoding is possible only when slot t _x is selected, since the absence of a click in the detectors when slot t ₃ is selected is much more likely to correspond to the loss of a photon in the channel than encoding zero in the Z-basis. Therefore, all events corresponding to the absence of a click in the detector must be discarded. Thus, in order to increase the efficiency (speed) of key transmission, it is possible to always encode only one state in the Z-basis, for example, Z, .

[0071] Obviously, the described QKD scheme, in essence, implements the BB84 protocol, therefore, it is possible to implement decoy states in it, for example, by installing an amplitude modulator at the output of the slave laser. It should also be remembered that Bob's interferometer (especially if it is implemented in a fiber version) requires temperature stabilization. It is also important to note that in this circuit, Bob does not need a fast phase modulator, since only one "phase" basis is used here. Thus, the use of Scheme I with the amplitude-phase modulator shown in FIG. Error! Reference source not found., allows you to get rid of expensive high-speed phase modulators in both Alice's optical circuit and Bob's optical circuit, which is an obvious advantage of this circuit.

[0072] The described process implements the possibility of decoding the transmitted pulses (photon quantum states) by the receiving device. In accordance with the description above, in a particular embodiment, the receiving device may contain a phase modulator that allows you to change the phase in one of the arms of the interferometer in a controlled way and select states in the phase basis, and at least one single photon detector, configured to operate in the gating mode, which is necessary to select the basis. [0073] Implementation of an amplitude-phase modulator. Scheme II

[0074] The optical design shown in FIG. 2 can be modified by removing the bandpass optical filter 7 from Alice's transmitter, as shown in FIG. Error! Reference source not found. We will call this scheme Diagram II. For a person skilled in the art it should be obvious that under the specified Scheme II is also understood as an amplitude-phase modulation device. Unlike Scheme I, where for amplitude modulation, the effect of phase locking is used, followed by optical filtering; in this optical scheme, amplitude modulation is realized by lowering the lasing threshold on the slave laser under the action of optical injection. Indeed, in the presence of a sufficiently intense field in the slave laser cavity, which is started from the master, the generation of intrinsic radiation in the slave laser begins at a lower carrier concentration than in the absence of external radiation, i.e. the master, as it were, "helps" to quickly gain the required field intensity for the transition from the spontaneous emission amplification mode to the laser generation mode.

Due to this effect, the bias current and modulation current on the slave laser can be chosen such that in the absence of radiation from the master, it does not "flare up", i.e. pulses would be generated only when optical injection was turned on. Such a mode of operation of the slave laser is shown in Fig. Error! Reference source not found. (a), where it can be seen that in the absence of pulses from the master, the controlled laser does not generate pulses.

[0075] In FIG. Error! Reference source not found. (a) Simulations of pulse sequences on the slave and master lasers are shown. To simulate optical signals, systems of equations (1) and (2) were used (without Langevin noise); in the simulations, the pulse repetition rate of the controlled laser is 1.25 GHz, and the bias currents on both lasers were set below the threshold value, i.e., both lasers were assumed to operate in the gain switching mode. From FIG. Error! The reference source was not found. (a) it can be seen that the mode of operation of the control laser does not differ from that used in Scheme I. Three types of pulses are again used here: short pulses used for time coding, and two types of long pulses (with a “pit ” and without a “hole”), which are used for phase coding. Phase and time coding are carried out here in the same way as in Scheme I, with the only difference that the amplitude modulation is implemented on a different effect. From FIG. Error! Reference source not found. (b) it can be seen that decoding is also carried out similarly to Scheme I: the signal corresponding to the interference of adjacent pulses is divided into frames; the choice of the basis is carried out by choosing a time slot inside the frame.

[0076] Scheme II has one very important difference that is not shown in FIG. Error! Reference source not found.(a) but becomes clear from FIG. Error! Reference source not found. FIG. Error! Reference source not found. (a) It can be seen that the slave laser pulses corresponding to the bit transmission in the phase basis (for example, a pair of pulses in Fig. Error! Reference source is not found. (a) in the range from 5 to 6 ns), differ noticeably in intensity: the second pulse has a lower intensity than the first (the difference in intensities is denoted here as

SQ). Such distinguishability of impulses, generally speaking, can be used by Eve in order to distinguish between bases or even encoded bits, i.e. can be used to attack. The shown difference in intensities SQ is due to the fact that, as mentioned above, optical injection reduces the generation threshold; therefore, as can be seen from Fig. Error! Reference source not found. (c), during the time when the master is on (for example, in the range from 5 to 6 ns in Fig. Error! Reference source not found.), the pump current pulse of the slave laser leads to an increase in the number of carriers N not up to the threshold value N _th (it is indicated by a dotted line in Fig. Error!

Link source not found.(c)), but to some lower value. Moreover, when the current pulse on the slave laser is turned off (Fig. Error! Reference source not found. (d)) the number of its carriers in the active layer will decrease faster than it was in the absence of optical injection. This is due to the fact that, in addition to the intrinsic relaxation of carriers, which is characterized by the lifetime of free electrons in the active layer, during optical injection, these carriers also interact with the radiation of the control laser, i.e. induced recombination takes place, leading to a decrease in the effective carrier lifetime. As a result, during the same time, the carrier concentration has time to decrease by a greater amount than it was in the absence of radiation from the master. Consequently, at the next current pulse, the number of carriers N begins to grow from a lower value. The difference between adjacent minima in the time dependence of the number of carriers in the range from 5 to 6 ns is indicated in Fig. Error! Reference source not found.(in) as SN . It is the difference SN that leads to a noticeable difference in the pulse intensities SQ. Based on this, it is quite obvious that this problem can be solved by slightly increasing the amplitude of the current pulse on the slave laser, as shown in Fig. Error! Reference source not found.(d). The change in current SI compensates for the difference SN, so that the second pulse in the pair corresponding to the bit transmission in the phase basis becomes almost indistinguishable from the first. On FIG. Error! The source of the reference was not found. (a) the slave laser pulses are shown with just such compensation for the modulation current.

[0077] Implementation of an amplitude-phase modulator. Scheme III

[0078] In schemes I and II, the selection of the basis and the state in the basis on the Alice side is carried out using a random number generator (RNG). However, a semiconductor laser operating in the gain-switching mode by itself can be a source of quantum randomness, therefore, it is possible to configure the optical scheme to use this randomness to prepare quantum states without resorting to the use of an external source of randomness. On FIG. Error! The reference source was not found, an optical scheme is shown in which the choice of the state in the phase basis (but not in the time basis) can be performed passively, i.e. without the use of an RNG (we will call it Scheme III or a special case of the implementation of an amplitude-phase modulation device). Unlike Scheme I

(Fig. Error! Reference source not found.), where the signal after the optical band-pass filter 7 (and after attenuation at the attenuator 8) is sent to the quantum channel, in Scheme

III signal of the slave laser after the optical band-pass filter 7 branches on a beam splitter (generally speaking, with an arbitrary division factor) and part of the signal is fed into an unbalanced interferometer, in which a preliminary measurement of the pulse interference is performed using a classical (not single-photon) detector 15. Note that the interferometer Alice is similar to Bob's interferometer, i.e. has the same delay line (this also assumes that Alice's interferometers and

Boba must be temperature stabilized). Note also that the phase modulator in Alice's interferometer is optional, so in FIG. Error! Reference source not found, missing.

[0079] The mode of operation of the control laser in Scheme III differs from the previous schemes. An example of an optical pulse train leaving the master and the corresponding slave laser pulse train (before they pass through the optical band pass filter) are shown in FIG. Error! Reference source not found.(a). The systems of equations (1) and (2) were used to simulate optical signals, this time with Langevin noise. It can be seen that two types of pulses are created on the master: short, with a duration approximately equal to the period Tp _of the slave laser pulses, and long, with a duration twice as long. Both types of pulses are now used for amplitude modulation. The latter is implemented, as in Scheme I, due to frequency filtering, but now the filter bandwidth must be chosen so that the transmission window corresponds to the eigenfrequency of the slave laser. The carrier frequency of the master pulses, on the other hand, should be set outside the bandwidth window. Then, due to the phenomenon of phase locking, the driven laser pulses that occur during optical injection will be filtered and will not fall into the quantum channel. The pulse train of the controlled laser after the bandpass filter is shown in Fig. Error! Reference source not found.(b). It can be seen that, as in the previous diagrams, the "filtered" sequence is grouped in pairs, between which there are "silent" impulses. If one of the pulses in the pair is empty, then this corresponds to the choice of the Z-basis, but if both pulses are present in the pair, then this corresponds to the choice of the X-basis. (To explicitly show that the state in the X-basis is not known before the measurement, we use in Fig. Error! Reference source not found. (b) for these states, the notation X _r , where the index r with some probability can take on the values 0 or 1 .) Switching between bases, as well as choosing a state in

The Z-basis in this scheme is carried out on the basis of a random sequence created by the RNG, which is part of the device, however, to select the state in the X-basis, the internal randomness of the phase between pulses associated with spontaneous emission is used. Thus, the preparation of phase states is carried out passively.

[0080] Since the phase difference between pulses in the "phase" basis is random, Alice must first measure this phase difference in order to know what state is sent to Bob. For these purposes, an interferometer with a photodetector 15 is used. The result of the interference of the pulses shown in FIG. Error!

Reference source not found. (b), shown in FIG. Error! Reference source not found. (c), where, as in the previous diagrams, the resulting sequence is divided into frames consisting of three time slots. From an experimental point of view, the measurement of the interference result on the Alice side corresponds to the measurement of the pulse intensity in the time slot t ₂ with its subsequent normalization to the intensity of the pulse in the time slot t ₃ (or /,). If the normalized value S of the interference signal is equal to 4 (naturally, with some error due to the imperfection of the measuring equipment), then the interference is constructive, if this value is equal to 0 - destructive. It should be noted here that for a more accurate measurement of the interference result, it is desirable to digitize the photodetector signal using an ADC with the largest possible bandwidth; narrow-band ADCs will significantly distort the shape of the pulse and will not allow you to accurately measure the value of the normalized signal S. It is also important to keep in mind that since Alice uses only one interferometer to measure the phase, the phase difference between the pulses can only be determined up to a sign, therefore, states with phase differences equal to p/2 and 3p/2 using one interferometer cannot be distinguished. Indeed, the value S = 2 corresponds to both of these states. Nevertheless, for ideal destructive interference (phase difference in the vicinity of p) and for ideal constructive interference (phase difference in the vicinity of 0), we can assume that the phase difference is determined quite uniquely.

[0081] So, if Alice measures destructive interference on her interferometer, then the state X ₀ can be assigned to the corresponding pair of pulses, if the interference turns out to be constructive, then the state X _x should be attributed to this state. Obviously, with this approach, most of the states in the phase basis will be discarded, so it makes sense to assign to the states X ₀ and X _x not only the results of ideal destructive ( S = 0 ) and constructive ( S = 4 ) interference, but also use values close to them S values. On the complex plane, this can be represented by a signal constellation in the form of two arcs centered around 0 and x, as shown in Fig. Error! Reference source not found. (d) on the right. The choice of the range of angles in this case should be determined by the choice of the QKD protocol. In particular, when using the BB84 protocol, this range should be limited by the value of the maximum allowable quantum error level (QBER) and, generally speaking, should be determined experimentally. So, in Fig. Error! Reference source not found. (d) The signal constellation is shown for the case when Alice assigns a set of states with a phase difference between pulses of 180° ±20° to the X ₀ state, which corresponds to the level of the normalized signal S from 0 to 0.12, and the state X _x - a set states with a phase difference of 0° ± 20°, which corresponds to the level of the normalized signal S from 3.88 to 4.

[0082] In FIG. Error! Reference source not found. (d) The left shows a simulation of the interference signal "measurement" results for the 8 frames shown in FIG. Error! Link source not found. (c) (frame number is written in its upper left corner in Fig. Error! Link source not found. (c)). Obviously, for frames corresponding to states in the Z-basis, the normalized signal has the value S = 1 (the corresponding values are indicated by hexagons). The remaining values of the normalized interference signal in FIG. Error! Reference source not found. (d) shown as empty circles. The angle values written next to the corresponding points were obtained using the formula:

On FIG. Error! Reference source not found. (d) it is clear that the state obtained in the 3rd frame falls within the range of angles we have chosen, so that the corresponding pair pulses can be attributed to the state X _x . The states measured in the remaining frames (## 4,7,8) will have to be discarded by Alice.

[0083] Implementation of an amplitude-phase modulator. Scheme IV

[0084] In the previous scheme, passive preparation of states was carried out only for the phase basis, while RNG was supposed to be used to select the state in the time basis. Scheme IV shown in FIG. Error! Link source not found., allows Alice to passively prepare any phase state, and thus completely get rid of the external source of randomness. The main difference from Scheme III shown in FIG. Error! The source of the reference was not found., here is the presence of two unbalanced interferometers, with the help of which it is already possible to unambiguously characterize the phase difference between the interfering pulses. We also note that in Scheme IV both interferometers have a phase modulator, however, unlike Bob's phase modulator, these modulators can be quite "slow" (and, therefore, relatively cheap), so their use does not contradict the main idea of the described optical schemes. .

[0085] The sequences of optical pulses exiting the master and slave lasers in Scheme IV (before they pass through the optical band pass filter) are shown in FIG. Error! Reference source not found.(a). Here, systems of equations (1) and (2) with Langevin noises were again used to simulate optical signals. It is assumed that both lasers operate in the gain switching mode and generate pulse sequences with different repetition periods: the repetition period of the master pulses is three times the repetition period of the slave laser pulses. As in Scheme III, the control laser pulses are used for amplitude modulation. The pulse train after the optical band pass filter is shown in Fig. Error! Reference source not found.(b). As should be clear from the above, in contrast to Scheme III, both bases in Scheme IV are phase. Indeed, in Fig. Error! Reference source not found. (b) The pulse sequence is divided into pairs of pulses with a random phase difference between them. To explicitly show that the generated states prior to measurement are not known, we use in FIG. Error! The reference source was not found. (b) for these states, the designation B _r , where B can take the values X , Y , and the index r can take the values 0 or 1.

[0086] To determine which state is being sent to Bob, Alice needs to measure the phase difference for each pair of pulses. To do this, she uses a system of two interferometers shown in Fig. Error! Reference source not found., which, in fact, play the role of a homodyne detector. Measurement of pulse interference in this scheme is carried out as follows. First, it is necessary to adjust the phase modulators 16 by setting such voltages on them that the phase differences between the interfering pulses in the two interferometers differ by 7r/2. If the Alice interferometers are identical, we can assume that one of the modulators 16 introduces a phase delay that is a multiple of 2p (i.e., 0), and the second modulator adds a phase shift p/2. The results of interference in two interferometers tuned in this way are shown in FIG. Error! Reference source not found.(c). Here, as in all previous schemes, the pulse sequence is divided into frames of three time slots. Due to the presence of "silent" pulses, the result of the interference corresponds to the slot t ₂ within the frame. The "measured" values of the intensity of the resulting pulses are shown by empty circles for an interferometer with a phase modulator introducing phase 0, and empty triangles for an interferometer with a phase modulator introducing a p/2 phase. On FIG. Error! Reference source not found. (d) on the left, the same designations are used for normalized values of interference results obtained in different frames. For definiteness, we will use the notation S _l for a normalized interference signal corresponding to an additional phase incursion of 0, and S ₂ for a normalized interference signal with a phase incursion p/2. As in Scheme III, the normalization is performed with respect to the intensity of the pulses in the time slot t ₃ (or t). (In order not to clutter up the figure, the time slots in Fig. Error! The reference source was not found. (c) are not signed, since they have the same designations as in the previous diagrams.) Having the values of the normalized interference signals S _x and

S ₂ for a given pair of pulses, the phase difference between them can be determined using the following formulas:

where 0 _t and f _: correspond to the possible values of the desired phase difference. The true value of the phase difference corresponds to the value q _: which coincides with one of the values f . WO 2023/282782 For example, if qf _c or q _c = f ₂ (in this case, the inequalities q ₂ f and

Q 2 _F f ₂ ), then the true value of the phase difference is equal to q _c . (Values

and f _c must be limited to the interval from 0 to 2n .) It is important to keep in mind, however, that in a real experiment all four values of the angles calculated using formulas (5) may turn out to be different due to noise in the measuring instruments and in the laser itself . Therefore, from a practical point of view, the “correct” value of q _c corresponds to the search for the minimum element of the sequence {q _c -f _c , q _c -f ₂ , q ₂ -f _c , q ₂ -f ₂ }. So, if the element q ₂ -f _c takes the minimum value, then the phase difference between the pulses should be set equal to ₂ .

[0087] The values of the phase difference between the respective pairs of pulses, determined by the method just described, are indicated next to the corresponding values of the normalized signals in FIG. Error! Reference source not found.(d). Since now Alice can determine the phase difference between the pulses exactly (i.e., she can distinguish between the states n/2 and Zl/2), she can use two non-orthogonal "phase" bases: X-basis, using the phase differences 0 and n for the states X _x and X ₀ , and U-basis using the phase difference l/2 and Zl/2 for the states U and U ₀ . However, as in

Scheme III, with such a choice of angles, Alice will have to discard most of the states, therefore it is advisable to use arcs rather than points on the complex plane as a signal constellation, as shown in Fig. Error! Reference source not found. (d) on the right. Here, for definiteness, we have chosen the central angles of all arcs to be 40°. On FIG. Error! Reference source not found. (d) on the left, it is shown that with this choice of angle range, three of the eight frames can be assigned certain states: Y _Q for frames ##2,6 and X ₀ for frame #1.

[0088] Some remarks and possible modifications of circuits I-III are not orthonormal (although they are orthogonal in each of the bases). Indeed, from Fig. Error! Reference source not found., Fig. Error! Reference source not found, and FIG. Error! The reference source has not been found, it can be seen that the pulse intensity in the X- and Z-basis is the same, which means that the states in the X-basis will, on average, have twice as many photons as the states in the Z-basis. Graphically, this can be represented by two Bloch spheres of different radii, as shown in Fig. Error! Reference source not found., where the poles of a sphere of smaller radius correspond to the states |Z ₀ and | Z, (in ket-bra notation), and points on the equator of a sphere of larger radius correspond to the states

and . If we assume that the sphere on which the states from the Z-basis are located has a unit radius, i.e. Z ₀ |Z ₀ ) = (Z, |Z,) = 1 , then the states | ₀ and |jf,} defined as

, respectively, have a norm equal to 2, (Х ₀ 1 ₀ ) = ( , | ,) = 2 , although still (Х ₀ |2Г) = 0. Generally speaking, the use of quantum states lying on different Bloch spheres does not correspond to the situation usually considered in the BB84 protocol, therefore, to calculate the key generation rate, it is necessary on the recipient side to independently collect statistics on the received pulses in different bases, similar to the so-called effective BB84, in which the bases are chosen with different probabilities.

[0090] Denote by P _i the probability of triggering the detector on Bob's side, provided that Alice's pulse contains / photons, then for a Poisson source with intensity n, the absolute probability will be expressed as

V i a e

R.

/! '

Thus, for an intensity signal n, the average detection probability is equal to

Similarly, we denote by e the conditional error probability in detecting the i-th photon pulse, then the absolute error probability is expressed as follows:

where E _v is the quantum bit error rate (QBER) at intensity n .

Let the basis X be used to generate the key, then the key generation rate is expressed by the following formula:

where is the correction efficiency function, usually taken as a constant,

// ₂ (x)

is the binary Shannon entropy. Denoting for V the intensity in the Z basis, we get 2v for the intensity in the X basis, then the experimental data Q _y and E _x correspond to the values of Qi _v and 2v, respectively. Q

(phase error of single-photon pulses in the X basis) needs to be evaluated, which can be done as follows:

In accordance with the obtained value of the key generation rate, the secrecy strengthening procedure and authentication verification are carried out, which completes the post-processing of the key. [0091] Note that the case under consideration can be easily reduced to a standard BB84 by adding an intensity modulator to the optical circuit. For the case of Scheme I, this is shown in FIG. Error! Reference source not found., where intensity modulator 17 is installed after the bandpass filter. The operation of the intensity modulator 17 becomes clear from FIG. Error! Reference source not found. (b), where it is seen that the pulses coming from the controlled laser are modulated in intensity so that the intensity of the pulse pair corresponding to the X-basis is halved. In this case, the states from the X- and Z-bases will be related as follows:

The result of combining such pulses in an interferometer with a delay line equal to the pulse repetition period is shown in Fig. Error! Reference source not found.(c).

[0092] Modification of Schemes II and III to equalize the amplitudes of states in different bases is carried out in a similar way: it is necessary to install an intensity modulator in the corresponding optical scheme, for example, as shown in Fig. Error! Reference source not found, (for Scheme II) and FIG. Error! Reference source not found, (for Scheme III). We also note that such a modification of optical schemes also makes it possible to implement the method of deceptive states.

[0093] Finally, we note that both the transmitting and receiving parties, obviously, must be equipped with an advanced system of electronic components that control the quantum key distribution device. These controllers are not shown in the drawings because they are not directly part of the optical circuit, and their specific implementation is beyond the scope of this description. We only note that the controller of the transmitting device must be configured to control laser drivers that set electrical pulses. _wo 2023/282782 sequences to the control and slave lasers, and the controller of the receiving device must be configured to control the broadband phase modulator in the interferometer arm and single photon detectors.

[0094] For example, in FIG. 16 shows a general view of the computing device (100), which may represent, for example, these controllers.

[0095] In general, the computing device (100) comprises one or more processors (101), memory devices such as RAM (102) and ROM (103), input/output interfaces (104), devices input/output (105), and a device for networking (106).

[0096] The processor (101) (or multiple processors, multi-core processor, etc.) can be selected from a range of devices currently widely used, for example, manufacturers such as: Intel ™, AMD ™, Apple ™, Samsung Exynos ™, MediaTEK™, Qualcomm Snapdragon™, etc. Under the processor or one of the processors used in the device (100), it is also necessary to take into account the graphics processor, for example, NVIDIA GPU or Graphcore, the type of which is also suitable for full or partial execution of the execution of the control module, and can also be used for training and applying machine learning models in various information systems.

[0097] RAM (102) is a random access memory and is designed to store machine-readable instructions executable by the processor (101) to perform the necessary data logical processing operations. RAM ( 102) typically contains the executable instructions of the operating system and associated software components (applications, program modules, etc.). In this case, the RAM (102) may be the available memory of the graphics card or graphics processor.

[0098] A ROM (103) is one or more persistent storage devices such as a hard disk drive (HDD), a solid state drive (SSD), flash memory (EEPROM, NAND, etc.), optical storage media ( CD-R/RW, DVD-R/RW, BlueRay Disc, MD), etc.

[0099] Various types of I/O interfaces (104) are used to organize the operation of the components of the computing device (100) and organize the operation of external connected devices. The choice of the appropriate interfaces depends on the specific design of the computing device, which can be, but not limited to: PCI, AGP, PS/2, IrDa, FireWire, LPT, COM, SATA, IDE, Lightning USB (2.0, 3.0, 3.1, micro, mini, type C), TRS/ Audio jack (2.5, 3.5, 6.35), HDMI, DVI, VGA, Display Port, RJ45, RS232, etc.

[0100] To ensure user interaction with the computing device (100), various means (105) of I/O information are used, for example, a keyboard, a display (monitor), a touch screen, a touchpad, a joystick, a mouse, a light pen, a stylus, touch panel, trackball, speakers, microphone, augmented reality, optical sensors, tablet, indicator lights, projector, camera, biometric identification tools (retinal scanner, fingerprint scanner, voice recognition module), etc.

[0101] The network communication means (106) provides data transmission via an internal or external computer network, for example, an Intranet, Internet, LAN, etc. As one or more means (106) can be used, but not limited to: Ethernet card, GSM modem, GPRS modem, LTE modem, 5G modem, satellite communication module, NFC module, Bluetooth and / or BLE module, Wi-Fi module and others

[0102] In these application materials, a preferred implementation of the claimed technical solution was presented, which should not be used as limiting other, private embodiments of its implementation, which do not go beyond the scope of the requested legal protection and are obvious to specialists in the relevant field of technology.

Sources of information:

[1] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, "Quantum cryptography," Rev. Mod. Phys., vol. 74, pp. 145-195, 2002.

[2] Z. L. Yuan, B. Frohlich, M. Lucamarini, G. L. Roberts, J. F. Dynes, and A. J. Shields, "Directly Phase-Modulated Light Source," Phys. Rev. X, vol. 6, p. 031044, 2016.

[3] R. Lang, "Injection locking properties of a semiconductor laser," IEEE J. Quantum. Elect. , vol. 18, pp. 976-983, 1982.

[4] S. Kobayashi and T. Kimura, "Optical phase modulation in an injection locked AlGaAs semiconductor laser," IEEE J. Quantum. Elect., vol. 18, pp. 1662-1669, 1982.

[5] G. L. Roberts, M. Lucamarini, J. F. Dynes, S. J. Savory, Z. L. Yuan, and A. J. Shields, "A direct GHz-clocked phase and intensity modulated transmitter applied to quantum key distribution," Quantum Science and Technology, vol. 3, p. 045010, 2018.

[6] TK ^Parai'so , I. De Marco, T. Roger, DG Marangon, JF Dynes, M. Lucamarini, Z. Yuan, and AJ Shields, "A modulator-free quantum key distribution transmitter chip," npj Quantum Information , vol. 5, p. 42, 2019. [7] R. Shakhovoy, M. Puplauskis, V. Sharoglazova, A. Duplinskiy, V. Zavodilenko, A. Losev, and Y. Kurochkin, "Direct phase modulation via optical injection: theoretical study," Opt. Express, vol. 29, pp. 9574-9588, 2021.

[8] A. G. J. MacFarlane, J. P. Dowling, and G. J. Milbum, "Quantum technology: the second quantum revolution," Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 361, pp. 1655-1674, 2003.

[9] C. H. Bennett and G. Brassard, "Quantum cryptography: Public key distribution and coin tossing," Theor. Comput. Set, vol. 560, pp. 7-11, 2014.

[10] W. K. Wootters and W. H. Zurek, "A single quantimi cannot be cloned," Nature, vol. 299, pp. 802-803, 1982.

[11] N. Lutkenhaus and M. Jahma, "Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack," New Journal of Physics, vol. 4, pp. 44-44, 2002.

[12] B. Huttner, N. Imoto, N. Gisin, and T. Mor, "Quantum cryptography with coherent states," Phys. Rev. A, vol. 51, pp. 1863-1869, 1995.

[13] W.-Y. Hwang, "Quantum Key Distribution with High Loss: Toward Global Secure Communication," Phys. Rev. Lett., vol. 91, p, 057901, 2003.

[14] H.-K. Lo, X. Ma, and K. Chen, "Decoy State Quantum Key Distribution," Phys. Rev. Lett., vol. 94, p. 230504, 2005.

[15] A. Duplinskiy, V. Ustimchik, A. Kanapin, V. Kurochkin, and Y. Kurochkin, "Low loss QKD optical scheme for fast polarization encoding," Opt. Express, vol. 25, pp. 28886-28897, 2017.

[16] R. Shakhovoy, D. Sych, V. Sharoglazova, A. Udaltsov, A. Fedorov, and Y. Kurochkin, "Quantum noise extraction from the interference of laser pulses in optical quantum random number generator," Opt. Express, vol. 28, pp. 6209-6224, 2020.

Claims

FORMULA

1. An amplitude-phase modulation device for quantum key distribution, configured to create quantum states in phase and time bases, comprising:

- a control laser configured to set the phase and time bases using optical pulses of different durations, wherein the state encoding in the phase basis is carried out using a perturbation of the pump current in the middle of a long pulse, and the state encoding in the time basis is carried out by selecting the short pulse generation time;

- an optical circulator configured to transmit radiation from the control laser to the controlled laser and output the radiation of the controlled laser to the optical attenuator.

2. The device according to claim. 1, characterized in that the output of the controlled laser additionally contains an intensity modulator designed to equalize the amplitude of the states in the time and phase bases.

3. The device according to claim 1, characterized in that the long pulses are unperturbed rectangular pulses and rectangular pulses with pump current perturbation in the middle.

4. The device according to claim. 1, characterized in that the long pulse from the control laser is shifted in time so that it starts earlier than the pulse of the controlled laser.

5. The device according to claim. 1, characterized in that it additionally contains an optical band-pass filter.

6. The apparatus of claim. 5, characterized in that the optical band pass filter is at least a passive fiber optic DWDM filter.

7. The device according to paragraphs. 5-6, characterized in that the transmission frequency of the optical band-pass filter is chosen so that all the radiation of the controlled laser in the absence of optical injection is completely absorbed.

8. The device according to claim 5, characterized in that it additionally contains an unbalanced interferometer.

9. The device according to claim 5, characterized in that it additionally contains two unbalanced interferometers.

10. The device according to claim 1, characterized in that the controlled and control lasers are at least semiconductor lasers coupled by optical injection.

11. The system of quantum key distribution (QDC), containing the device according to any one of paragraphs. 1-10, connected via a quantum communication channel with a receiving device, and:

- a device according to any one of paragraphs. 1-10 further comprises: o an optical attenuator configured to attenuate the signal before it is transmitted to the quantum channel; o a controller configured to control laser drivers that set electrical pulse sequences to the control and slave lasers;

12. The system according to claim 11, characterized in that the time window (frame) allocated for the quantum state contains at least three time slots.

3. The system according to claim 11, characterized in that the selection of the basis by the receiving device is carried out by at least sending a strobe pulse to at least one single photon detector in a certain time slot of the time window of the quantum state.