KR102308058B1 - Reference-frame-independent measurement-device-independent quantum-key-distribution communication system using fewer quantum states - Google Patents

Abstract

According to the present specification, disclosed is an RFI-MDI-QKD communication system using a small number of quantum states compared to a conventional RFI-MDI-QKD communication system. In a conventional RFI-MDI-QKD protocol, each of Alice and Bob must transmit six quantum states. However, the RFI-MDI-QKD communication system according to the present specification can have a similar level of stability to a conventional system even when Alice and Bob transmit only quantum states of 2-4 or 1-4.

Description

RFI-MDI-QKD communication system using a small number of quantum states

The present invention relates to an RFI-MDI-QKD communication system, and more particularly, to an RFI-MDI-QKD communication system using a small number of quantum states compared to a conventional RFI-MDI-QKD communication system.

The explosive development of quantum computer technology that can implement Shor's algorithm, which can effectively solve the factorization problem, and Grover's algorithm, which reduces the search time in the database, is a modern cryptography based on computational complexity. It means that it may no longer be safe. Quantum cryptography is a representative technology that is safe even in a quantum computing environment because it is based on the basic principles of quantum mechanics. Quantum Key Distribution (QKD), which can safely share the same secret key among communication members, is a representative protocol of quantum cryptography.

One of the efforts to improve the security and practicality of the QKD protocol is measurement-device-independent QKD (MDI-QKD). MDI-QKD is a protocol for sharing a secret key through Bell State Measurement (BSM), which can determine the correlation of photons transmitted by Alice and Bob. Even if Charlie, an unreliable third party, or eavesdropper Eve, knows the BSM result, it cannot extract information about the shared secret key without the encoding information of Alice and Bob. Therefore, MDI-QKD can provide safety regardless of the measuring device. In addition, there is an additional advantage that the communication distance can be increased.

Meanwhile, in general, Alice and Bob need a reference frame to perform the QKD protocol. For example, in the case of free space QKD (free space QKD), the polarization axes or the relative phase difference of interferometers are shared between Alice and Bob, or fiber-based communication. In the case of , time-bin qubits must be shared. However, sharing such a frame of reference is difficult and expensive in itself, and in particular, in the case of free space QKD using satellite, it is not easy to maintain the polarization axis. Furthermore, it is becoming difficult to share a reference frame in QKD communication with a large number of participants.

To solve this problem is a quantum key distribution (Reference-Frame-Independent QKD, RFI-QKD) communication protocol that is independent of the reference frame. The RFI-QKD communication protocol is a communication protocol that improves the practicality of QKD communication. In RFI-QKD, the secret key is shared through a base that is not affected by rotation and fluctuation of the reference frame, and security is confirmed by the other two non-commuting bases.

The concept of RFI can be applied to MDI-QKD and implemented as RFI-MDI-QKD to provide high practicality and high security for QKD communication.

C. Wang et al., "Reference-Frame-Free experiment of Measurement-Device-Independent Quantum Key Distribution" Phys. Rev. Lett. 115, 160502 (2015).

An object of the present specification is to provide an RFI-MDI-QKD communication system using a smaller number of quantum states compared to the conventional RFI-MDI-QKD communication system.

The present specification is not limited to the above-mentioned problems, and other problems not mentioned will be clearly understood by those skilled in the art from the following description.

RFI-MDI-QKD communication system according to the present specification for solving the above-mentioned problems, a first communication device having a public channel for transmitting a quantum state to a quantum channel and receiving the bell measurement state information; a second communication device having a public channel for transmitting a quantum state through a quantum channel and receiving bell measurement state information; and a third communication for transmitting the measurement result of the bell state of both the quantum channel of the first communication device and the quantum channel of the second communication device to the first communication device and the second communication device through a public channel. device; includes. In this case, the first communication device includes an interferometer for generating an arbitrary phase difference between the X-axis and the Y-axis of the quantum state emitted from the light source; and a first modulator for modulating the z-axis of the quantum state emitted from the light source. And the second communication device, the interferometer for generating an arbitrary phase difference between the X-axis and the Y-axis of the quantum state emitted from the light source; a second modulator located on either optical path in the interferometer; and a third modulator for modulating the z-axis of the quantum state emitted from the light source.

According to an embodiment of the present specification, each interferometer included in the first communication device and the second communication device may form two optical paths having different lengths by using two beam splitters.

In this case, the second modulator included in the second communication device may be disposed on a relatively longer optical path among two different optical paths in the interferometer.

In addition, the second modulator included in the second communication device may be a phase modulator.

According to an embodiment of the present specification, the first modulator included in the first communication device and the third modulator included in the second communication device may be intensity modulators.

In this case, the interferometer included in the first communication device may be disposed between the light source and the first modulator, and the interferometer included in the second communication device may be disposed between the light source and the third modulator.

According to an embodiment of the present specification, the light source may be a laser.

In this case, each of the first communication device and the second communication device may include an attenuator.

According to an embodiment of the present specification, the third communication device includes: a beam splitter through which quantum states transmitted from the first communication device and the second communication device pass together; two polarization beam splitters for detecting a polarization direction according to a polarization direction of a quantum state that has passed through the beam splitter; and a detector that detects the quantum detected by each polarization beam splitter.

According to an embodiment of the present specification, in the first communication device, a modulator for modulating a phase is not disposed on all optical paths in the interferometer.

Other specific details of the invention are included in the detailed description and drawings.

According to one aspect of the present specification, the quantum secret key can be distributed using a smaller number of quantum states compared to the conventional RFI-MDI-QKD communication system. Accordingly, the device can be more simplified while having stability similar to that of the conventional RFI-MDI-QKD communication system.

Effects of the present invention are not limited to the effects mentioned above, and other effects not mentioned will be clearly understood by those skilled in the art from the following description.

1 is a conceptual diagram of MDI-QKD.
2 is a schematic configuration diagram of a conventional RFI-MDI-QKD communication system.
3 is a schematic configuration diagram of an RFI-MDI-QKD communication system according to the present specification.
4 is an experimental configuration diagram of an RFI-MDI-QKD communication system according to the present specification.
5 is an experimental result of the RFI-MDI-QKD communication system.

Advantages and features of the invention disclosed herein, and methods of achieving them, will become apparent with reference to the embodiments described below in detail in conjunction with the accompanying drawings. However, the present specification is not limited to the embodiments disclosed below, but may be implemented in various different forms, and only the present embodiments allow the disclosure of the present specification to be complete, and those of ordinary skill in the art to which this specification belongs. It is provided to fully inform those skilled in the art (hereinafter 'those skilled in the art') the scope of the present specification, and the scope of the present specification is only defined by the scope of the claims.

The terminology used herein is for the purpose of describing the embodiments and is not intended to limit the scope of the present specification. As used herein, the singular also includes the plural unless specifically stated otherwise in the phrase. As used herein, “comprises” and/or “comprising” does not exclude the presence or addition of one or more other components in addition to the stated components.

Like reference numerals refer to like elements throughout, and "and/or" includes each and every combination of one or more of the recited elements. Although "first", "second", etc. are used to describe various elements, these elements are not limited by these terms, of course. These terms are only used to distinguish one component from another. Accordingly, it goes without saying that the first component mentioned below may be the second component within the spirit of the present invention.

Unless otherwise defined, all terms (including technical and scientific terms) used herein may have the meaning commonly understood by those of ordinary skill in the art to which this specification belongs. In addition, terms defined in a commonly used dictionary are not to be interpreted ideally or excessively unless specifically defined explicitly. Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The RFI-MDI-QKD communication system according to the present specification can have the same stability and security as the conventional RFI-MDI-QKD communication device even using a small number of quantum states compared to the conventional RFI-MDI-QKD communication device. characteristic. In order to better understand the RFI-MDI-QKD communication system according to the present specification, the MDI-QKD communication device will be briefly described first.

1 is a conceptual diagram of MDI-QKD.

Referring to FIG. 1 , Alice and Bob arbitrarily set bit values (+ or -) on the X, Y, and Z axes and transmit them to a third person, Charlie. Six quantum states are possible with three axes and two bit values.

Charlie performs a Bell state measurement (BSM) and reports the result to Alice and Bob, respectively. And Alice and Bob can generate a quantum key using the information when photons are sent in the same direction using the BMS result. At this time, it is important that the general MDI-QKD shares a reference frame among Alice, Bob, and Charlie.

If Alice, Bob, and Charlie do not share a reference frame, as shown in FIG. 1 , consider a case in which three axes are related. In this case, the 3-axis is as shown in Equation 1 below.

<Formula 1>

는 찰리를 기준으로 하는 상대적 기준 프레임 회전이고, S는 A(앨리스) 또는 B(밥)이다. 통신 시스템을 구성하는 모든 구성원 즉, 앨리스, 밥 및 찰리에게 Z축은 기준 프레임 회전에서 변화하지 않기 때문에 앨리스와 밥은 Z축을 사용하여 임의의 비트 스트링을 분배할 수 있다. 반면, X축과 Y축에서 BSM는 제어할 수 없는

과 관련 있기 때문에, 일반적인 MDI-QKD의 성능을 제한하는 양자 비트 오류율(QBER, Quantum Bit Error Rate)은 증가하게 된다.

is the relative frame of reference rotation with respect to Charlie, and S is either A (Alice) or B (Bob). For all members of the communication system, namely Alice, Bob, and Charlie, since the Z axis does not change in the rotation of the frame of reference, Alice and Bob can use the Z axis to distribute any string of bits. On the other hand, in the X and Y axes, the BSM cannot be controlled.

, the quantum bit error rate (QBER), which limits the performance of general MDI-QKD, increases.

The RFI-MDI-QKD communication device is a communication protocol for solving this problem of MDI-QKD. The RFI-MDI-QKD communication device is a quantum key distribution protocol that can secure the safety and practicality of quantum key distribution by combining the advantages of RFI-QKD and MDI-QKD. In terms of safety, it guarantees safety against all kinds of quantum hacking attempts on the photon qubit measurement unit, and in terms of practicality, QKD communication is possible without reference frame alignment. To this end, the RFI-MDI-QKD communication protocol introduces a new frame rotation invariant parameter 'C' and uses the C-parameter to confirm the security of the quantum communication channel. The C-parameter is given as in Equation 2 below.

<Formula 2>

를 의미한다.

상태는 앨리스와 밥이 비밀키를 생성하기 위해 전송되므로, 앨리스와 밥은 모두 6개의 임의의 상태 중 하나의 양자 상태를 전송해야 한다. 이때, BMS 결과값은 아래 수식 3과 같이 정의될 수 있다.In Equation 2, the subscript '44' represents the four quantum states that Alice and Bob must transmit to measure the C-parameter.

means

Since the state is sent by Alice and Bob to generate the secret key, both Alice and Bob must send one quantum state out of six random states. In this case, the BMS result value may be defined as in Equation 3 below.

<Equation 3>

는

와

의 입력에 따른

의 BMS 결과를 의미한다. 따라서, 수식 3의 분모는 모든 입력 상태에 대한 BMS 결과의 합을 의미한다.M and N are X and Y, A is Alice, B is Bob, i and j are + and -,

Is

Wow

according to the input of

of BMS results. Therefore, the denominator of Equation 3 means the sum of the BMS results for all input states.

The secret key ratio can be measured together with the C-parameter and QBER on the X and Z axes, Q _X , Q _{Z .} In general MDI-QKD, the secret key ratio is given as in Equation 4 below.

<Formula 4>

H[X] is the Shannon entropy of X. Therefore, in RFI-MDI-QKD, the secret key ratio is given as in Equations 5 and 6 below.

<Formula 5>

<Formula 6>

Summarizing the contents up to this point, in terms of practicality, the RFI-MDI-QKD communication device is not a single photon light source, but a weakly attenuated laser pulse and a decoy state. However, for RFI-MDI-QKD safety analysis, quantum bit error rate (QBER) and C-parameter values must be extracted through experiments. To this end, both communication devices Alice and Bob must transmit one quantum state out of six random states.

As mentioned above, the RFI-MDI-QKD communication system according to the present specification provides the same stability and security as the conventional RFI-MDI-QKD communication device even using a small number of quantum states compared to the conventional RFI-MDI-QKD communication device. It's a feature you can have. Hereinafter, how to reduce the quantum number will be explained.

를 얻기 위한 BMS 결과 확률은

의 측정이다.

와

는 앨리스와 밥의 입력 상태이다. 따라서 이를 종합하면 아래 표 1과 같다.

The BMS result probability to obtain is

is the measurement of

Wow

is the input state of Alice and Bob. Therefore, it is summarized in Table 1 below.

<Table 1>

이다. 상기 수식 2에 사용된 값 사이에서 아래 수식 7과 같은 관계를 유도할 수 있다.in table 1

am. A relationship as shown in Equation 7 below can be derived between the values used in Equation 2 above.

<Formula 7>

According to Equation 7, Alice can omit the Y-axis quantum state for obtaining the C-parameter. If Alice omits the Y-axis quantum state, Equation 2 for the C-parameter is the same as Equation 8 below.

<Equation 8>

와 밥이 전송해야 하는 4가지 양자 상태

를 의미한다.In Equation 8, the subscript '24' is the two quantum states that Alice must transmit to measure the C-parameter.

and 4 quantum states that Bob must transmit

means

Furthermore, in Table 1, a relationship such as Equation 9 below can be found.

<Equation 9>

Through this, Alice can reduce the quantum state by one more. Therefore, Equation 8 regarding the C-parameter is the same as Equation 10 below.

<Equation 10>

와

의 3가지 양자 상태만 전송하면 충분하다.According to Equation 10, in order to perform the RFI-MDI-QKD protocol, Alice

Wow

It is sufficient to transmit only three quantum states of

2 is a schematic configuration diagram of a conventional RFI-MDI-QKD communication system.

은 빠른 타임-빈(fast time-bin

),

은 느린 타임-빈(slow time-bin

)에 해당한다.

와

는 광펄스가 간섭계의 어떤 경로를 통과하느냐에 의해 결정되므로, IM을 이용해 하나의 경로를 막아서 생성될 수 있다.

,

,

,

는 광자의 확률진폭이

와

모두에 있을 때,

와

사이의 위상에 따라 결정될 수 있다. 따라서 간섭계 내부의 PM을 이용하여 임의의 위상을 인코딩(encoding)해야한다.Referring to FIG. 2 , a time-bin encoding RFI-MDI-QKD communication system may be identified. The light source is a laser, BS is a beam splitter, IM is an intensity modulator, and PM is a phase modulator. In Time-bin encoding

is the fast time-bin

),

is the slow time-bin

) corresponds to

Wow

Since is determined by which path of the interferometer the light pulse passes, it can be generated by blocking one path using IM.

,

,

,

is the probability amplitude of the photon

Wow

when in everyone,

Wow

It can be determined according to the phase between them. Therefore, it is necessary to encode an arbitrary phase using the PM inside the interferometer.

3 is a schematic configuration diagram of an RFI-MDI-QKD communication system according to the present specification.

,

중 하나의 양자상태를 전송할 수 있다.

상태는 간섭계를 구성하기만 하면 생성되며, PM이 불필요하다. PM이 없으면

값이 임의의 한 값으로 고정되며, 어떤 값으로 고정되더라도 RFI-MDI-QKD를 구현할 수 있음은 앞서 수식 1 내지 수식 10을 통해 충분히 설명하였으므로 반복적인 설명은 생략하도록 한다.Referring to FIG. 3 , it can be seen that the Bob side is the same, but the Alice side has the PM omitted compared to the conventional Alice side. Alice is

,

One of the quantum states can be transmitted.

The state is created by simply configuring the interferometer, no PM required. Without PM

The value is fixed to any one value, and the fact that RFI-MDI-QKD can be implemented no matter what value is fixed has been sufficiently described through Equations 1 to 10 above, so a repetitive description will be omitted.

Meanwhile, although FIG. 3 shows an example in which the PM on Alice's side is omitted, an embodiment in which the PM on Bob's side is omitted is also possible. When the PM of Bob's side is omitted, the Alice side is the same as the conventional RFI-MDI-QKD communication system.

<Experimental example>

4 is an experimental configuration diagram of an RFI-MDI-QKD communication system according to the present specification.

The same single photon at 1556 nm used by Alice and Bob is prepared by type II spontaneous parametric down-conversion using a 10 mm periodic polled KTP crystal pumped by a femtosecond laser pulse (not shown). The pump power and repetition rate of the pump are 10mW and 125MHz, respectively. Using superconducting nanowire single photon detectors (SNSPDs) with 80% of the single photon detection efficiency, approximately 200 kHz match. The distinction of single photons is confirmed by the Hong-Ou-Mandel (HOM) interference visibility of V~0.99. With high HOM visibility, even multi-photon-generated events can be ignored.

과

의 랜던 편광 상태가 인코딩된다. 단일 광자는 빔 스플리터(BS) 및 편광 빔 스플리터(PBS)를 사용하여 BSM을 수행하는 찰리에게 전송된다. 회전 양자 채널(

와

)을 정확하게 구현하기 위해, 양자 채널의 자유 공간에 파장판(waveplate)를 배치시켰다. 두 개의 1/4파장판 사이에 위치한 반파장판을 45도 회전시켜서, 수식 1의 기준 프레임 회전을 구현할 수 있다. 기준 프레임 회전 양자 채널의 효과를 조사하기 위해, 고정된

에 대한

에 대하여 MDI-QKD 및 RFI-MDI-QKD를 모두 수행하였다.by a set of half- and quarter-wave plates (H, Q)

class

The random polarization state of is encoded. A single photon is sent to Charlie performing BSM using a beam splitter (BS) and a polarizing beam splitter (PBS). rotating quantum channel (

Wow

), a waveplate was placed in the free space of the quantum channel. By rotating the half-wave plate positioned between the two quarter-wave plates by 45 degrees, rotation of the reference frame of Equation 1 can be implemented. To investigate the effect of a frame-rotated quantum channel of reference, a fixed

for

For both MDI-QKD and RFI-MDI-QKD were performed.

5 is an experimental result of the RFI-MDI-QKD communication system.

=0이고, 오른쪽 열은

=π/2인 데이터이다.Referring to FIG. 5 , the left column is

= 0, the right column is

= π/2 data.

의 다양한 기대값을 나타낸다. 가변하는

하에서

로 변하지 않는 동안, 모든 기대값은 V=0.945±0.002의 가시성을 가진 정현파 진동을 보여준다. 정현파 진동은 BSM를 위한 찰리의 BS에서 이상적이지 않는 위상 계수로 인해 표 1의 이론적 값에서 위상 변이가 있다. 이 역시, 수식 7을 증명한다.5 (a) and (e) are

represents the various expected values of . variable

under

while not changing, all expected values show sinusoidal oscillations with visibility of V = 0.945 ± 0.002. The sinusoidal oscillations have a phase shift from the theoretical values in Table 1 due to the non-ideal phase coefficients in Charlie's BS for BSM. This also proves Equation 7.

Referring to (b) and (f) of FIG. 5 , it is possible to estimate QBER in various axes with expected values. On the X and Y axes, QBER shows sinusoidal oscillations, but the Z axis does not change. The experimentally obtained Z-axis QBER is Q _Z =0.7-0.1%.

하에서 C-파라미터가 불변함을 명백하게 확인할 수 있다. 더 중요한 것은, C₄₄, C₂₄ 및 C₁₄의 C-파라미터가 서로 아주 유사하다는 것이다. 구체적으로 C₄₄=1.77±0.03, C₂₄=1.77±0.02 및 C₁₄=1.77±0.003이다.Referring to (c) and (g) of Figure 5, it can be confirmed the C-parameter. variable

It can be clearly seen that the C-parameter is unchanged under More importantly, C ₄₄ , C ₂₄ and The C _{-parameters of C 14} are very similar to each other. Specifically, C ₄₄ =1.77±0.03, C ₂₄ =1.77±0.02 and C ₁₄ =1.77±0.003.

에 따라 다르며 일부 영역에서는 positive 비밀 키를 생성하지 못한다. 반면에 RFIMDI-QKD는 임의이

에서도 항상 비밀 키를 생성할 수 있다. 또한 비밀키 생성 비율 r₄₄, r₂₄ 및 r₁₄가 매우 유사하다는 것은 적은 양자 상태를 사용하는 본 명세서에 따른 RFI-MDI-QKD 통신 시스템의 성능이 비슷하다는 것을 나타낸다.Finally, (d) and (h) of Figure 5 shows the secret key ratio (r). The general MDI-QKD secret key generation speed is

, and it is not possible to generate a positive secret key in some areas. On the other hand, RFIMDI-QKD is arbitrary.

can always generate a secret key. In addition, the fact that the secret key generation ratios r ₄₄ , r ₂₄ and r ₁₄ are very similar indicates that the performance of the RFI-MDI-QKD communication system according to the present specification using a small quantum state is similar.

In the above, the embodiments of the present specification have been described with reference to the accompanying drawings, but those of ordinary skill in the art to which this specification belongs can realize that the present invention may be embodied in other specific forms without changing the technical spirit or essential features thereof. you will be able to understand Therefore, it should be understood that the embodiments described above are illustrative in all respects and not restrictive.

Claims (10)

a first communication device having a public channel for transmitting a quantum state to a quantum channel and receiving bell measurement state information;
a second communication device having a public channel for transmitting a quantum state to a quantum channel and receiving bell measurement state information; and
A third communication device for transmitting the measurement result of the bell state of both the quantum channel of the first communication device and the quantum channel of the second communication device to the first communication device and the second communication device through a public channel In the RFI-MDI-QKD communication system comprising;
The first communication device includes: an interferometer for generating an arbitrary phase difference between the X-axis and the Y-axis of the quantum state emitted from the light source; and a first modulator for modulating the z-axis of the quantum state emitted from the light source;
The second communication device includes: an interferometer for generating an arbitrary phase difference between the X-axis and the Y-axis of the quantum state emitted from the light source; a second modulator positioned on either optical path in the interferometer; and a third modulator for modulating the z-axis of the quantum state emitted from the light source;
The RFI-MDI-QKD communication system, characterized in that the first communication device transmits a quantum state according to the following equation without a modulator for modulating a phase on all optical paths in the interferometer.

,

: fast time-bin

: slow time-bin
θ: any phase (θ)

) The method according to claim 1,
Each interferometer included in the first communication device and the second communication device,
An RFI-MDI-QKD communication system that uses two beam splitters to form two optical paths of different lengths. 3. The method according to claim 2,
The RFI-MDI-QKD communication system, characterized in that the second modulator included in the second communication device is disposed on a longer optical path among two different optical paths in the interferometer. 3. The method according to claim 2,
The RFI-MDI-QKD communication system, characterized in that the second modulator included in the second communication device is a phase modulator. The method according to claim 1,
The RFI-MDI-QKD communication system, characterized in that the first modulator included in the first communication device and the third modulator included in the second communication device are intensity modulators. 6. The method of claim 5,
The interferometer included in the first communication device is disposed between the light source and the first modulator,
The RFI-MDI-QKD communication system, characterized in that the interferometer included in the second communication device is disposed between the light source and the third modulator. The method according to claim 1,
The RFI-MDI-QKD communication system, characterized in that the light source is a laser. 8. The method of claim 7,
The RFI-MDI-QKD communication system further comprising a; each of the first communication device and the second communication device is an attenuator. The method according to claim 1,
The third communication device,
a beam splitter through which quantum states transmitted from the first communication device and the second communication device pass together;
two polarization beam splitters for detecting a polarization direction according to a polarization direction of a quantum state that has passed through the beam splitter; and
RFI-MDI-QKD communication system comprising a; detector for detecting the quantum detected in each polarizing beam splitter. delete

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