RU2794954C1 - Method and device for generating quantum states for protocols with distributed phase coding - Google Patents

Abstract

FIELD: quantum distribution of encryption keys.

SUBSTANCE: invention relates to generating a sequence of coherent pulses in protocols with distributed phase coding. A device for generating quantum states for protocols with distributed phase coding includes a pulsed laser, an optical ring resonator, including a beam splitter, an intensity modulator, a phase modulator, an attenuator, an electronic control device configured to generate and supply control signals to intensity and phase modulators with duration, equal or greater duration of the optical pulse, control delays between the control signals applied to the laser, phase modulator and intensity modulator, select the quantum state using a random number generator.

EFFECT: eliminating the influence of the temporal coherence of the laser on the number of optical pulses in the quantum state for protocols with distributed phase coding; reduction of energy consumption in the formation of quantum states for protocols with distributed phase coding; narrowing the bandwidth of the intensity modulator.

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Description

Field of the invention The present invention relates to the field of quantum distribution of encryption keys, in particular for generating a sequence of coherent pulses in protocols with distributed phase coding (differential phase shift, DPS).

State of the art

In quantum key distribution (QKD) systems, protocols with phase encoding are widely used. The advantages of this approach include the insensitivity of quantum states to polarization in the fiber line, which leads to a simplification of the design of the receiving side. Among these protocols, the distributed phase encoding (DPS) protocol can be distinguished. The advantage of this protocol is its simplicity, namely: the minimum number of phase modulator levels (0, π) simplifies system setup, in addition, there is no need for a random number generator and active electro-optical devices (phase modulator, polarization controller) on the receiving side.

The protocol can be described as follows. The transmitter (Alice) distributes the photon into a sequence of coherent optical pulses separated by a time interval Δ. Bit encoding is carried out using a phase modulator, which is activated when each optical pulse of the sequence passes through the modulator. The resulting sequence is called a quantum state. The choice of applied phases (0 or i) is made on the basis of a random sequence of a random number generator. Decoding and interpretation of the encoded information is carried out by the receiver (Bob). To do this, an interferometer with an optical path difference equivalent to the time interval Δ between pulses is installed in the receiver. In this case, adjacent pulses will interfere at the outputs of the interferometer depending on the encoded phase difference. Interpretation (detection) is carried out using single-photon detectors installed at the outputs of the receiver interferometer.

A description of the implementation of the protocol has been made in the publication (K. Inoue, E. Waks, Y. Yamamoto: "Differential Phase Shift Quantum Key Distribution", Phys. Rev. Lett., 89(3), 037902, 2002). According to the publication, a photon from a source of single (single) photons is divided into three parts in a three-beam Mach-Zehnder interferometer (IMC). Time delays in the shoulders in relation to the shortest are A and 2A. The division coefficients in the arms of the IMC provide equiprobable passage of a photon along any of the paths. After leaving the MMC, a photon contained in a sequence of three pulses equally spaced from each other in time enters the phase modulator. Further, the phase of each of the pulses in the sequence is randomly modulated by a phase modulator to 0 or π.

The resulting quantum state is sent to the receiver, which has a two-arm MMC with a similar time delay Δ. The receiver interferometer has two outputs, on which detectors are installed. A photon distributed over three sequence pulses can be registered by detectors in one of four time windows. Bob remembers the numbers of time windows in which the detector was triggered. After the transmission session is completed, Bob tells Alice the numbers of the time windows in which the detectors were triggered, but does not name which detector was triggered. Based on this information, the parties form an identical bit string - a secret key.

It is noted that the efficiency of the protocol in creating one E _bit (key creation efficiency) can be increased by increasing the number of MCI arms. Indeed, the efficiency of the protocol in producing one bit is expressed by the following formula

where N is the number of pulses in the quantum state.

Accordingly, as the number of pulses increases, the parameter E _bit also increases.

An increase in the efficiency of E _bit is possible by increasing the number of interferometer arms, however, such an increase is associated with technological difficulties in ensuring the equality of the division coefficients of the arms and the time delays between them. We also note that the MMC used is a passive device and does not allow changing the number of pulses in the sequence.

It is also worth noting that the existing sources of single photons operating in the telecommunications wavelength range have a low photon generation efficiency that does not meet the needs of the developed QKD systems. Therefore, laser radiation is used that is attenuated to a quasi-single-photon level close to a single-photon level. Note that modern lasers used to implement QKD have a generation threshold that is several orders of magnitude higher than required to obtain the required quantum state, so most of the radiation is lost as a result of attenuation to the quasi-single-photon level.

A method and device for generating a sequence of pulses in the QKD system are known (China application CN 1897519, priority dated May 30, 2006, - https://patentscope.wipo.int/search/en/detail.jsf?docld=CN83090069&_cid=P11- L3JV0F-53205-1), while the device contains series-connected

continuous laser (CW),

intensity modulator (IM),

polarizer,

phase modulator,

attenuator.

Continuous laser radiation is fed into the intensity modulator. The modulation is carried out in such a way that at the output of the modulator there is a sequence of optical pulses of the same power, equally spaced from each other by time A. Then the sequence of pulses is subjected to phase modulation, then attenuated to the required power level (number of photons per pulse) and sent to the recipient.

Note that the specified transmitter allows you to change the number of pulses in the quantum state, thus it is possible to increase the efficiency of the E _bit protocol.

Known device and method are taken as a prototype.

The disadvantages of the method include the fact that the time interval between pulses and their number in quantum states are limited by the temporal coherence of the laser.

In addition, the disadvantage of this method is that the temporal parameters of the optical pulses, namely the duration, are set by the intensity modulator. Accordingly, when forming short optical pulses, an intensity modulator and its control electronics with a wide bandwidth are required.

Indeed, in most QKD systems, an avalanche photodetector operating in a gated mode is used to register quantum states on the receiving side. One way to reduce the number of false positives of the photodetector due to dark currents is to reduce the gating time interval. Reducing the gating time interval dictates the need to reduce the duration of optical pulses used to form quantum states. For example, we note the study (B. Da Lioa, Baccob D. Cozzolino Y, Ding K., Dalgaard K. Rottwitt K., Oxenlowe L.K. Experimental demonstration of the DPTS QKD protocol over a 170 km fiber link, Applied Physics Letters, 114, 011101 , 2019; https://doi.org/10.1063/l.5049659), which indicated that the creation of short optical pulses of the order of 150 picoseconds was achieved using an intensity modulator. However, this required a high-speed intensity modulator driver that generates electrical pulses with a duration of 100 ps, which complicates and increases the cost of the circuit. In addition, the jitter (jitter) of the control electronics of the modulator can lead to a spread in the phases of the optical pulses of the quantum state.

Also, the disadvantages of the prototype include increased energy consumption in the formation of a quantum state. When forming a sequence of optical pulses from continuous radiation using an intensity modulator, the time interval between pulses is blocked by the modulator, and the duration of the blocked time interval increases with increasing pulse repetition rate at a constant duration of the generated pulses. Further, a multiple increase in the number of pulses in quantum states requires a multiple increase in the operating time of the laser and, accordingly, a multiple increase in energy consumption. Thus, the energy expended in generating a quantum state in the prototype is directly proportional to the number of pulses and their duty cycle.

Disclosure of invention

The technical result is:

1) elimination of the effect of laser temporal coherence on the number of optical pulses in a quantum state for protocols with distributed phase coding;

2) reduction of energy consumption in the formation of quantum states for protocols with distributed phase coding;

3) the possibility of narrowing the bandwidth of the intensity modulator.

To this end, a device is proposed that includes

pulse laser,

an optical ring resonator having an input and an output and including a beam splitter with two inputs and two outputs,

intensity modulator,

phase modulator,

attenuator,

electronic control device associated with the laser, phase modulator and intensity modulator and configured to

- formation of control signals applied to the laser, intensity modulator and phase modulator,

- supply of control signals to the intensity and phase modulators with a duration equal to or greater than the duration of the optical pulse,

- regulation of delays between the control signals applied to the laser, the phase modulator and the intensity modulator, about the choice of a quantum state using a random number generator,

and

- the pulsed laser is connected to the input of the optical ring resonator,

- the output of the optical ring resonator is connected to the input of the intensity modulator,

- the output of the intensity modulator is connected to the input of the phase modulator,

- the output of the phase modulator is connected to an attenuator,

while in the optical ring resonator,

- the first input of the beam splitter is the input of the resonator, o the second output of the beam splitter is the output of the resonator, o the first output and the second input of the beam splitter are connected, o the time of the light bypassing the resonator is greater than or equal to the duration of the optical pulse, o the optical pulse arriving at the first input of the beam splitter passes to the first output beam splitter with a transmittance T and is reflected to the second output of the beam splitter with a reflectance R, and T+R=1. The device implements a method for generating quantum states, which consists in the fact that

set the required number of pulses N in the quantum state,

set the number d equal to the ratio of the power of the residual pulse in the resonator to the power of the pulse coming from the laser to form a new quantum state,

set the number of pulses b, which are blocked before the formation of a new quantum state,

set the reflection coefficient of light power in the beam splitter of the optical resonator R, satisfying the condition R≤d ^1/(N-1+b) ,

using a random number generator, a bit string of length N is formed,

laser generates an optical pulse, power P _las ,

form a quantum state consisting of N coherent optical pulses, performing the following actions:

- an optical pulse with power P _las is fed to the input of the ring resonator,

- receive at the output of the ring resonator a sequence of optical pulses,

- block the optical pulse power P ₀ =P _las ⋅R using the intensity modulator,

- the power of each subsequent optical pulse P _n is weakened by the intensity modulator by the value R ^N-1 , where n is the pulse number in the sequence, n=1, 2…N,

- block the intensity modulator b pulses with numbers greater than N,

- receive at the output of the intensity modulator a sequence of N pulses with the same power P _las ⋅T ² ⋅R ^N-1 ,

- transmit the received sequence of optical pulses to the phase modulator,

- apply to the phase modulator a control signal corresponding to the value in the bit string,

- the resulting sequence of phase-modulated optical pulses is transmitted to the input of the attenuator for attenuation to a quasi-single-photon level, o a quantum state is obtained at the output of the attenuator,

direct the generated quantum state to its destination.

The scheme of the proposed device is shown in the figure of the graphic image.

When preparing a quantum state using a pulsed laser 1, an optical pulse of duration t and power Pias is formed. Then the specified pulse is fed to the input of the optical resonator 2. Moreover, the light in the resonator returns to the resonator due to reflection from the beam splitter. The resonator roundtrip time by light will be called the time delay and denoted by Δ, with Δ>τ.

When a laser pulse arrives at the resonator input, part of the light, determined by the reflection coefficient R of the beam splitter, is reflected to the second output of the beam splitter, connected to the input of intensity modulator 3. The rest of the light continues to propagate inside the resonator. After each bypass of the resonator by an optical pulse, a part of its power, proportional to the transmittance T of the beam splitter, passes through the beam splitter and enters the intensity modulator, and the second part, proportional to the coefficient R, remains in the resonator.

Thus, at the second output of the beam splitter, a sequence of M optical pulses occurs, separated by a time interval A. The power of each pulse in the sequence is described by the following expression:

It can be seen from the presented sequence (2) that all terms, except M ₀ (numbering starts from zero) with power P _las ⋅ R, which has not passed through a closed path, form a decreasing geometric progression, that is, the power of the pulses decreases with increasing their serial number from coefficient R.

To achieve maximum efficiency of the E _bit protocol and at the same time minimize the possibility of compromise by an attacker, the following sequence of actions is implemented.

First, the required number of pulses N in the quantum state is specified. Sequence (2) is decreasing, therefore, in order to obtain a sequence of coherent optical pulses of the same power, it is necessary to reduce the power of each pulse to one value, namely, to the power of the pulse with number N. To do this, the pulse M ₀ is blocked by the intensity modulator, the next pulse M ₁ s power Plas⋅T ² is attenuated R ^N-1 times, subsequent pulses M _N are attenuated R ^N " ⁿ times. The last pulse in the sequence Mn has a power P _las ⋅T ² ⋅R ^N-1 and is not attenuated by the intensity modulator equals R ^NN =T).

Since the sequence (2) is infinite, then, formally, the power of the outgoing pulses never reaches zero. This means that after the formation of a quantum state from N pulses, residual radiation will propagate in the resonator and, as a result, a residual sequence of pulses decreasing in power will be formed at the output. To reduce the effect of residual radiation on the subsequent quantum state (imposition of pulses), a number d is set, which expresses the allowable ratio of the power of the residual pulse in the resonator to the power of the pulse coming from the laser to form a new quantum state.

There must be a gap between neighboring quantum states that is a multiple of the time interval A. For this, the number b is set, which is equal to the number of blocked pulses after the formation of the current quantum state.

Based on the given parameters, the reflectance of the beam splitter is selected according to the following condition:

Thus, after blocking the pulse M ₀ =P _las ⋅R, which did not pass through a closed path, modulating the power of a series of N pulses and then blocking b pulses, it is allowed to form the next quantum state. As a result of these actions, at the output of the intensity modulator there will be a sequence of N pulses of equal power P _las ⋅T ² ⋅R ^N-1 , separated by a time interval Δ.

Further, the phase of each of the pulses in the sequence is randomly modulated by a phase modulator 4 to 0 or π. The attenuation of the quantum state to the required number of photons is carried out using an attenuator 5. The quantum state obtained at the output of the attenuator is sent to a fiber optic communication line with a receiver of quantum states.

Let us show that in the proposed device, the number of optical pulses in the quantum state for protocols with distributed phase coding is not limited by the temporal coherence of the laser.

Indeed, the DPS protocol assumes that the photon is distributed equally among the pulses of the quantum state, that is, the probability of its being in any pulse of the sequence is the same. In addition, such a distribution implies that all state pulses are coherent with each other (Mandel L., Volf E. Optical coherence and quantum optics. M .: Fizmatlit, 2000, p. 120). It is known that the temporal coherence of any laser is limited. That is, if in the prototype the temporal coherence of a continuous laser turns out to be less than the duration of the entire quantum state Δ⋅N (the totality of all time delays between pulses and their durations), then not all pulses in the quantum state will be coherent to each other. In turn, in the proposed device, all pulses in the sequence are formed by the amplitude division method, therefore they are coherent with each other.

Thus, the number of optical pulses in the proposed device and method is not limited by the temporal coherence of the laser.

Let us show that the proposed device has better energy efficiency than the prototype when forming a quantum state.

Let it be required to form a quantum state with energy E _q and consisting of N pulses. Each pulse has a duration τ. Duty cycle, i.e. the ratio of the pulse repetition period to their duration, denoted by S. Let us assume that the power of laser radiation is the same in both cases, that is, the laser generates radiation with energy E _las during time τ. The attenuator and intensity modulator are configured in such a way as to achieve in each case a quantum state with energy E _q at the output. In the prototype, for the formation of a quantum state from continuous radiation, a laser will generate radiation with energy E _cw =E _las ⋅(S⋅(N-1)+1). After passing through the intensity modulator and attenuator, the radiation is attenuated to the energy E _q . The energy efficiency of the prototype is expressed as the ratio η _cw =E _q /E _cw . When using the proposed scheme with a ring resonator to form the specified quantum state, the laser generates a laser pulse with duration τ and energy E _las , which is distributed in the sequence of pulses described by expression (2). Similarly to the prototype, after passing through the intensity modulator and the attenuator, the pulse sequence is attenuated to a total energy E _q . The energy efficiency of the proposed device is equal to η _r =E _q /E _las .

From the above formulas, we obtain that the ratio of the efficiency of the proposed device and the prototype is equal to η _r /η _cw =(S⋅(N⋅1)+1). Since the duty cycle is S≥1, and the number of pulses, according to formula (1), must be N≥2, the efficiency ratio will always be η _r/ η _cw ≥2.

We will show that the bandwidth of the intensity modulator in the proposed device may be lower than in the prototype for any duty cycle.

Consider the prototype and the claimed device under the same conditions, namely, let the duration of the optical pulses be the same and equal to τ. Then for the operation of the prototype it is necessary that the bandwidth of the intensity modulator was either BW _cw ≥1/τ when S≥2, or BW _cw >1/(τ(S-1)) when S<2. In turn, for the claimed device, the condition is the same for any duty cycle BW _r ≥1/(S⋅τ).

Thus, for any duty cycle, the condition BW _cw ≥BW _r is satisfied, which confirms the possibility of narrowing the bandwidth of the intensity modulator.

It can be noted that in the proposed method for obtaining a quantum state from N pulses of the same power, the first pulse in the quantum state can correspond to any pulse from the sequence of pulses at the output of the resonator. For example, instead of the pulse M ₁ =P _las ⋅T ^2, you can choose the next M ₂ =P _las ⋅T ² ⋅R, then the output will be a sequence of N pulses of equal power P ₀ ⋅T ² ⋅R ^N and separated by an interval time Δ.

We also note that it is possible, by making appropriate changes to the sequence of actions, not to block the impulse М ₀ with power P _las ⋅R, but to use it to form a quantum state. In addition, it is assumed that the intensity modulator introduces an attenuation different from 1 for the pulse number N. By adjusting this attenuation, one can change the energy of the quantum state, which is proportional to the average number of photons. In addition, power modulation can be performed in various ways. It is possible that a continuous function of time can be used for attenuation.

Distinctive features of the proposed device and method are that a ring resonator located between the laser and the intensity modulator is used to form a sequence of coherent optical pulses that form a quantum state.

The claimed technical result is achieved due to the fact that the formation of coherent pulses is implemented using the amplitude division method, and the required number of pulses in the quantum state can be set by controlling the intensity modulator.

Brief description of the drawings

The figure of the graphic image shows a diagram of a device in which the proposed method is implemented, in which the following designations are used (solid lines indicate optical connections, dotted lines indicate electrical connections):

1 - pulsed laser,

2 - ring resonator,

3 - intensity modulator,

4 - phase modulator,

5 -attenuator,

6 - electronic control device.

Implementation of the invention

In the general case, it is possible to perform a device with radiation propagation in free space.

Preferably, the device is made using fiber-optic components, while the part of the circuit from the laser to the phase modulator should be made on the basis of a polarization-preserving fiber.

As a pulsed laser, a semiconductor laser with distributed feedback is used with radiation output into a polarization-preserving fiber, and, for example, with linear polarization along the slow axis of the fiber. To implement the invention, you can use a laser type DFB-1550-14BF manufacturer JSC "Nolatech" (http://nolatech.ru/).

The ring resonator can be made on the basis of a 2x2 fiber beam splitter, the input and output of which are interconnected. The ring resonator is configured in such a way that the optical pulse arriving at the first input of the beam splitter passes to the first output of the beam splitter with a coefficient T and is reflected to the second output of the beam splitter with a coefficient R.

To implement the invention, a beam splitter of the PMFBTC-P-2x2-1550-L-50-PM-90 type manufactured by "DK Photonics" (http://www.dkphotonics.com/) can be used.

Equalization of the power of optical pulses, as well as the formation of a sequence with a given number of pulses N, can be carried out by an intensity modulator of the type MX-LN-05-PD-P-P-FA-FA manufactured by "iXblue" (https://www.ixblue.com/).

For phase modulation, an electro-optical modulator of the MPZ-LN-01-P-P-FC-FC type from the manufacturer "iXblue" (https://www.ixblue.com/) can be used.

An attenuator is used to attenuate optical pulses to a quasi-single-photon level. To implement the invention, an attenuator of the MOVA-1-D-C-FS type, manufactured by "Santec" (https://sphotonics.ru/), can be used.

One of the embodiments of the invention implies that the electronic control unit (ECU) 6 is built on the basis of an electronic computer (computer) with a network communication interface. In addition, the ECU contains a laser driver and drivers for a phase modulator and an intensity modulator, a clock pulse generator, and a random number generator. All necessary calculations on a computer to implement the method are implemented using software (software). Such specialized software can be formed by a programmer (programmer) based on known information about the device functions and actions that underlie the proposed method. Also, the electronic control device must be configured to adjust the delays between the control signals applied to the laser, the phase modulator and the intensity modulator, and to supply control pulses to the phase and intensity modulators.

After assembling the optical and electronic parts, the transmitter is launched in the operating mode. When connected to the communication line with the receiver, the transmitter reports the number of pulses in the quantum state N=7, and the receiver transmits a signal of readiness to receive a sequence of quantum states via the network interface.

For each packet of coherent pulses, the random number generator generates a bit string of length N=7, corresponding to the number of pulses in the quantum state. This string is transmitted to the computer, where it is compared to the phase modulator control signals, which correspond to a phase shift of 0 or π radians. Then set the number d=0.5 ¹⁰ and the number of blocked pulses b=4. From expression (3) it follows that R<0.5, therefore, to implement the method, a beam splitter with R=T=0.5 is selected.

To generate a quantum state with a laser, a single optical pulse is generated, which is fed to the input of the ring resonator. The output is a sequence of optical pulses. In this case, the optical pulse M ₀ with power P _las ⋅ 0.5 is blocked by the intensity modulator, the next pulse M ₁ with power Plas ⋅ 0.5 ² is attenuated by 0.5 ⁶ times and each subsequent pulse is attenuated by the intensity modulator by 0.5 ^{7- n} times, n=1, 2, … 7, where n is the number of the current impulse. Thus, the power of each of the seven pulses will be equal to P _las ⋅0.5 ⁸ . After passing through the pulse intensity modulator with the number N=7, the subsequent series of b=4 pulses is blocked.

The resulting sequence of seven pulses is fed to the phase modulator. The computer instructs the phase modulator driver such that each sequence pulse passing through the phase modulator is phase-shifted 0 or to, according to the bit string mapping, into the phase modulator control signals.

After that, the sequence enters the input of the attenuator, where it is attenuated to a quasi-single-photon level. The quantum state obtained at the output of the attenuator is sent through a fiber-optic communication line to the receiver of quantum states.

There are other options for implementing the proposed device and method, depending on preferences when choosing hardware and software. For example, in the closed path of the ring resonator, an optical switch can be installed to interrupt the train of optical pulses, or a tunable delay line to change the time delay Δ between optical pulses.

Claims (32)

1. A device for generating quantum states for protocols with distributed phase coding, including a pulsed laser, optical ring resonator, having an input and an output and including a beam splitter with two inputs and two outputs, intensity modulator, phase modulator, attenuator, an electronic control device associated with the laser, phase modulator and intensity modulator and configured to generate control signals applied to the laser, intensity modulator and phase modulator, supply of control signals to the intensity and phase modulators with a duration equal to or greater than the duration of the optical pulse, adjusting the delays between the control signals applied to the laser, the phase modulator and the intensity modulator, selecting a quantum state using a random number generator; and the pulsed laser is connected to the input of the optical ring resonator, the output of the optical ring resonator is connected to the input of the intensity modulator, the output of the intensity modulator is connected to the input of the phase modulator, the output of the phase modulator is connected to an attenuator; while in the optical ring resonator the first input of the beam splitter is the input of the resonator, the second output of the beam splitter is the output of the resonator, the first output and the second input of the beam splitter are connected, the resonator roundtrip time is greater than or equal to the duration of the optical pulse, the optical pulse arriving at the first input of the beam splitter passes to the first output of the beam splitter with a transmittance T and is reflected to the second output of the beam splitter with a reflection coefficient R, with T+R=1. 2. A method for generating quantum states, which consists in setting the required number of pulses N in a quantum state; set the number d, equal to the ratio of the power of the residual pulse in the resonator to the power of the pulse coming from the laser to form a new quantum state; set the number of pulses b, which are blocked before the formation of a new quantum state; set the reflection coefficient of light power in the beam splitter of the optical resonator R, satisfying the condition R≤d ^1/(N-1+b) ; using a random number generator, a bit string of length N is formed; generate laser optical pulse power P _las ; form a quantum state consisting of N coherent optical pulses, performing the following actions: submit an optical pulse power P _las to the input of the ring resonator; receive at the output of the ring resonator a sequence of optical pulses; blocking the optical pulse power P ₀ =P _las ⋅R using the intensity modulator; attenuate the power of each subsequent optical pulse P _n by the intensity modulator by R ^Nn , where n is the pulse number in the sequence, n=1, 2…N; block intensity modulator b pulses with numbers greater than N; get at the output of the intensity modulator a sequence of N pulses with the same power P _las ⋅T ² ⋅R ^N-1 ; transmitting the received sequence of optical pulses to the phase modulator; submitting to the phase modulator a control signal corresponding to the value in the bit string; transmitting the received sequence of phase-modulated optical pulses to the input of an attenuator for attenuation to a quasi-single-photon level; a quantum state is obtained at the output of the attenuator; direct the generated quantum state to its destination.

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