All-passive quantum key distribution apparatus, method and key rate estimation method thereof

Abstract

The application discloses a kind of full passive quantum key distribution device, method and its key rate estimation method, arbitrary quantum state of sending end arbitrary quantum coherent state on Bloch sphere is generated by passive generation module, first reflection light after first beam splitter is used to carry out polarization direction measurement and quantum state post-selection, first transmission light after first beam splitter enters the local detection response module;In local detection response module, the transmission light of second beam splitter enters receiving end, and reflection light is divided into two single-photon detectors by beam splitting, and the corresponding photon number distribution model is established using the response and non-response events of single-photon detector;According to polarization direction, photon number distribution model and the measurement result of receiving end, the secure key of receiving end is obtained.The application avoids the intensity detection error caused by signal state and decoy state distinction.Can realize higher security key rate.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of quantum key distribution device and method, especially passive quantum key distribution device and method. BACKGROUND

[0002] Quantum key distribution technology (QKD, Quantum key distribution) is shared by the user in remote two places through the transmission of quantum state and the key is used to strictly encrypt information once in a way, which provides us with a kind of unconditional secure communication mode based on information theory principle.Current QKD implementation provides relatively less protection to the side channel in light source, and these side channels are generally considered to be trusted.In fact, modulator may inadvertently leak information during encoding process.Trojan horse attack (THA, Trojan-Horse Attack) is a kind of attack mode launched against the sending end side channel, and in THA process, Eve sends strong light signal to Alice, and tries to obtain information about the setting from the reflected light to steal the key.Although a large amount of optical isolation can be carried out on the quantum channel of the sending end to resist THA eavesdropping to some extent, there are obvious difficulties in its specific implementation.

[0003] An alternative solution to eliminate THA once and for all is to consider using a completely passive QKD transmitter, and this QKD scheme is passive quantum key distribution. -3 to 10 -2 It is difficult to accurately measure the light intensity of quantum state, and the imperfection of device leads to the decrease of secure key rate; at the same time, the transmittance of different state settings in transmission channel may be detected by eavesdropper Eve and then security risk is generated, and trace distance constraint method is adopted in prior art to represent the above risk and include it into security analysis, which also leads to the decrease of secure key rate. SUMMARY

[0004] The purpose of the present application is to provide a kind of passive quantum key distribution device and method based on local detection response, which does not need to select different light intensity signal state and decoy state by dividing photon intensity interval, avoids the intensity detection error caused by signal state and decoy state division, and can realize higher secure key rate at longer transmission distance.Meanwhile, the present application also provides a kind of key rate estimation method.

[0005] Technical scheme: the passive quantum key distribution device provided by the present application, the sending end includes arbitrary quantum state generation module and local detection response module.

[0006] The arbitrary quantum state generation module generates an arbitrary quantum coherent state on a Bloch sphere passively by using a linear optical system, first reflected light after the first beam splitter is used for polarization direction measurement and post-selection of the quantum state, and first transmitted light after the first beam splitter enters the local probe response module;

[0007] In the local probe response module, second transmitted light after the second beam splitter enters a receiving end, second reflected light after the second beam splitter enters a third beam splitter, and two beams of light obtained after the third beam splitter enter two single-photon detectors respectively, and a photon number distribution model is established by using response and non-response events of the single-photon detectors;

[0008] In the receiving end, two-way signals after the second polarization beam splitter enter an H state detector and a V state detector respectively, and measurement results are obtained; and a security key is obtained according to the polarization direction of the sending end, the photon number distribution model and the measurement results of the receiving end.

[0009] Further, in the arbitrary quantum state generation module, four incident lights with the same intensity and different random phases are input to the linear optical system, and two first incident light and second incident light with orthogonal polarization states are obtained; the first incident light and the second incident light are input to the first beam splitter, and the first incident light and the second incident light are taken as the north pole and the south pole of the Bloch sphere, an RL-Bloch sphere is obtained, and an arbitrary quantum coherent state with random phase, random intensity and random polarization direction in the RL-Bloch sphere is output, and the intensity and the polarization are coupled with each other.

[0010] Further, probability density functions of the phase, the intensity and the polarization direction of the quantum coherent state satisfy:

[0011]

[0012] Wherein, v represents an average light intensity of the incident light, t represents a beam splitting ratio of the first beam splitter, and φ ∈ (-π, π], θ ∈ [0, π], I ∈ [0, I max,θ ), φ represents an azimuth angle of the RL-Bloch sphere, θ represents a polar angle of the RL-Bloch sphere, I represents an average photon number of the first transmitted light after the first beam splitter, f θ,I (θ, I) represents a joint probability density function of the quantum state polar angle and the average light intensity.

[0013] Further, the sending end and the receiving end agree that linear polarization directions 0 and π in the RL-Bloch sphere constitute a Z basis, and linear polarization directions constitute an X basis; the sending end determines an acceptable polar angle change amount Δθ and an acceptable azimuth angle change amount Δφ according to a distance between the sending end and the receiving end, and performs post-selection of the quantum state, and the quantum state after the post-selection is:

[0014]

[0015] wherein, r represents Fock state photon number, k represents linear polarization direction of quantum state, i.e.

[0016] Further, the two beams of light obtained after the second reflected light enters the third beam splitter enter the first single photon detector and the second single photon detector respectively, and four kinds of response events are generated according to the triggering results of the first single photon detector and the second single photon detector, and are denoted as X1-X4 respectively:

[0017] X1: neither the first single photon detector nor the second single photon detector responds;

[0018] X2: the first single photon detector responds, and the second single photon detector does not respond;

[0019] X3: the second single photon detector responds, and the first single photon detector does not respond;

[0020] X4: both the first single photon detector and the second single photon detector respond;

[0021] The event X i The transmission signal sent to the receiving end when the event X The density matrix projected into the photon number space.

[0022] Further, the sender performs post-selection of the quantum state to obtain a group of quantum state random key sequences and a group of corresponding base selection sequences, the random key sequence is sent to the receiving end, and the base selection sequence is published; the receiving end selects a random sequence to determine a measurement base to obtain a measurement result sequence; and the receiving end compares the base selection sequence with the measurement result sequence to obtain a security key.

[0023] Further, the third beam splitter is a variable beam splitter.

[0024] The full passive quantum key distribution method provided by the application comprises the following steps:

[0025] The arbitrary quantum state generation module of the sender passively generates an arbitrary quantum coherent state on a Bloch sphere by using a linear optical system, and the first reflected light after the first beam splitter is used for polarization direction measurement and post-selection of the quantum state; the first transmitted light after the first beam splitter enters the local detection response module;

[0026] The second transmitted light enters the receiving end after the first transmitted light passes through the second beam splitter, and the second reflected light after the second beam splitter enters the third beam splitter to obtain two beams of light entering two single-photon detectors, respectively, and a corresponding photon number distribution model is established by using the response and non-response events of the single-photon detector;

[0027] In the receiving end, the two signals of the second transmitted light after passing through the second polarization beam splitter enter the H-state detector and the V-state detector, respectively, to obtain a measurement result; and the security key is obtained according to the polarization direction of the sending end, the photon number distribution model and the measurement result of the receiving end.

[0028] Further, the system security key rate R is:

[0029]

[0030] Wherein, represents the probability that the signal state is a single-photon state when the event X i occurs, and H2(x) is a binary Shannon entropy function. EC represents the system error correction efficiency, e1 is the single-photon error code number, y1 is the single-photon transmittance, and respectively represent the system gain and system error code number of the event X i , is the probability that the arbitrary quantum state generated by the linear optical system is located in the post-selection region Ω k .

[0031] Further, the single-photon transmittance is calculated by solving a linear programming problem:

[0032] min f=y1

[0033]

[0034] 0≤y n ≤1(n=1,2,…,9)

[0035] The single-photon error rate is calculated by solving a linear programming problem:

[0036] max f=e1

[0037]

[0038] 0≤e n ≤1(n=1,2,…,9)

[0039] Wherein, n represents the number of photons of the transmitted quantum state, y n represents the transmittance of the quantum state with n photons, and e n represents the error code number of the quantum state with n photons.

[0040] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows: The present invention adopts a fully passive method in the key transmission stage, which does not require modulation of light source intensity or division of photon intensity range. This not only eliminates the intensity modulation error that may be caused by intensity modulation, but also avoids potential information leakage caused by modulation signal light intensity. Furthermore, it can use a local single-photon detection system to obtain four different response events, record and use these four different response events for compact estimation and accurate calculation, so that the secure key rate and the maximum transmission distance that can be generated under the given security conditions are significantly increased. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the fully passive quantum key distribution device of the present invention.

[0042] Figure 2 This is a secure key rate-distance image according to an embodiment of the present invention. Detailed Implementation

[0043] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0044] like Figure 1 As shown, the fully passive BB84 quantum key distribution device includes user terminals Alice and Bob, as well as a channel, where user terminal Alice acts as the transmitter and Bob acts as the receiver.

[0045] The transmitting end Alice is divided into an arbitrary quantum state passive generation module and a local detection response module.

[0046] In the arbitrary quantum state passive generation module, all input coherent states used by Alice have the same intensity v and independent random phases α, β, γ, δ. Unused spatial modes are represented by the symbol... The beam interferes in the 50:50 beam splitter BS of the upper (lower) arm of the linear optical system, generating a coherent state with random intensity. The intensity of this state is related to the phase difference β-α(δ-γ), while the polarization of the two input beams in the upper (lower) arm remains the same and unchanged. In this embodiment, the upper arm has right-hand circularly polarized light, and the lower arm has left-hand circularly polarized light; the two are orthogonal to each other. The orthogonally polarized coherent pulses enter the first polarization beam splitter PBS1, outputting arbitrary quantum coherent states with random phase, random intensity, and random polarization direction in the RL-Bloch sphere, with intensity and polarization mutually coupled. Specifically, the probability density functions of the quantum state phase, intensity, and polarization direction satisfy:

[0047]

[0048] where v represents the average output intensity of the laser, t represents the splitting ratio of the beam splitter BS1, and φ ∈ (-π, π], θ ∈ [0, π], I ∈ [0, I max,θ ), and

[0049]

[0050] It can be seen that the joint probability density function f θ,I (θ, I) reaches the extreme value at .

[0051] Then, the random quantum state enters the first beam splitter BS1 with a splitting ratio t << 1 so that the transmission intensity is greatly attenuated, and the first reflected light output by the first beam splitter BS1 enters the polarization analyzer, which can accurately measure the polarization direction thereof for the sender to perform the post-selection of the quantum state.

[0052] The sender Alice selects the right circularly polarized light and the left circularly polarized light as the north pole and the south pole of the Bloch sphere, and at this time, the equatorial plane of the sphere contains all possible linearly polarized single-photon states, and the specific linear polarization direction is determined by the azimuth angle of the sphere, so that all the generated arbitrary single-photon states collectively constitute an “RL-Bloch sphere”.

[0053] Alice and Bob agree on a common quantum linear polarization direction as the 0 state through a classical secure secret channel, and select the linear polarization directions 0, π in the RL-Bloch sphere to constitute the Z basis of the BB84 protocol, and the linear polarization directions constitute the X basis. The sender Alice determines the optimal acceptable polar angle variation Δθ and the acceptable azimuth angle variation Δφ according to the distance between the communication parties. Alice performs the post-selection of the quantum state with the equatorial plane of the sphere, i.e. as the center, and with the linear polarization directions 0, π, as the center of the post-selection region of the quantum state. At this time, the post-selected quantum state can be represented as:

[0054]

[0055] where r represents the Fock state photon number, k represents the linear polarization direction of the quantum state, i.e. φ represents the azimuth angle of the RL-Bloch sphere, θ represents the polar angle of the RL-Bloch sphere, I represents the average photon number of the transmitted light after the first beam splitter BS1, i.e., before entering the local detection response system, and f θ,I (θ, I) represents the joint probability density function of the polar angle and the average intensity of the quantum state.

[0056] For the sake of brevity, the <·> symbol is used to represent that any input expression ′·′ is integrated by f Ω in the space region Ω composed of (φ, θ, I).φ,θ,I (φ,θ,I) = f θ,I (θ,I) / 2π weighted triple integral, i.e.

[0057]

[0058] In the local detection response module, the transmitted light generated by the first beam splitter BS1 is called the first transmitted light, and the first transmitted light is made to enter the second beam splitter BS2 with a beam splitting ratio of t0. The reflected light generated by the second beam splitter BS2 is called the second reflected light, and the second reflected light is made to enter the third beam splitter VBS with a beam splitting ratio of t1. v The variable third beam splitter VBS is further divided into two parts, which are respectively sent into two local single-photon detectors, and all response and non-response events from the local single-photon detectors are used to establish corresponding different photon number distribution models. Specifically, the two beams of light are respectively collected by the two single-photon detectors D1 and D2 arranged locally; four response events are generated according to the trigger results of the detectors, and are respectively denoted as X1-X4:

[0059] X1: neither D1 nor D2 responds;

[0060] X2: D1 responds and D2 does not respond;

[0061] X3: D2 responds and D1 does not respond;

[0062] X4: both D1 and D2 respond.

[0063] After Alice completes the local measurement and post-selection of the quantum state, a set of quantum state random key sequences {a n} and a set of corresponding base selection sequences {x n} can be obtained. The random key sequence is transmitted to Bob through a quantum channel. In the channel model of the present scheme, the quantum transmission loss η ch and the detection loss η det of the detection end are collectively equivalent to η, i.e. η = η ch η det , and the polarization rotator PR is used to represent the measurement base selection of Bob. When the measurement base selected by Bob is the Z base, the quantum signal is decomposed into two signals with orthogonal polarization directions by the polarization beam splitter PBS2 and is sent to the H state and V state detectors respectively. After receiving a set of quantum states, Bob announces this fact and selects a set of random sequences {y n} of the same length to determine the measurement base, and the measurement result is recorded as the sequence {b n}.

[0064] Alice announces her base selection sequence {x n}, and Bob compares it with his own measurement base selection {y nThe two are compared, and the same position of the two is informed to Alice, and the different data of the two is discarded.

[0065] The full passive quantum key distribution method comprises the following steps.

[0066] The arbitrary quantum state generation module of the sending end passively generates an arbitrary quantum coherent state on a Bloch sphere by using a linear optical system, the first reflected light after the first beam splitter is used for polarization direction measurement and quantum state post-selection, and the first transmitted light after the first beam splitter enters the local detection response module;

[0067] In the local detection response module, the second transmitted light after the first transmitted light passing through the second beam splitter enters the receiving end, the second reflected light after the second beam splitter enters the third beam splitter, and then two beams of light enter two single-photon detectors respectively, and a corresponding photon number distribution model is established by using the response and non-response events of the single-photon detector;

[0068] In the receiving end, the two-way signal after the second transmitted light passing through the second polarization beam splitter enters the H state detector and the V state detector respectively, and a measurement result is obtained; and a secure key is obtained according to the polarization direction of the sending end, the photon number distribution model and the measurement result of the receiving end.

[0069] The key rate estimation method comprises the following steps.

[0070] The present application defines the event X i , and the transmission signal under the condition of the event X i , i = 1, 2, 3, 4. The transmission signal is projected into a photon number space, and the density matrix of the photon number space is

[0071]

[0072] wherein represents the photon number distribution probability of the signal state when the event X i occurs.

[0073] Assume that the number of photons of the quantum state entering the second beam splitter BS2 after the sender Alice sends the light beam is r, and m photons are reflected by BS2 into the local single-photon detection response system and n photons are transmitted by BS2 into the quantum transmission channel, so r = m + n, and the quantum state at this time can be expressed as:

[0074]

[0075] The probability of the number of photons of the quantum state entering the second beam splitter BS2 being r is:

[0076]

[0077] wherein, represents the creation operator of the linear optical system for generating an arbitrary quantum state, respectively represent the creation operators of the transmitted light and the reflected light of the beam splitter BS2, and T1, R1 are the corresponding normalization coefficients. At this time, the quantum state mapped through the beam splitter BS2 can be rewritten as:

[0078]

[0079] At this time, the diagonal items of the density matrix of the quantum state are:

[0080]

[0081] Therefore, in the case that the number of photons of the quantum state entering the second beam splitter BS2 is r, the joint probability of m photons being reflected by BS2 into the local detection response system and n photons being transmitted by BS2 into the transmission channel is:

[0082]

[0083] Therefore, when the sender Alice sends information, the joint probability of m photons being reflected by BS2 into the local single-photon detection response system and n photons being transmitted by BS2 into the quantum transmission channel is:

[0084]

[0085] Meanwhile, assume that the local single-photon detector of the sender Alice is completely ideal, that is, the detection efficiency is 100%, and under this assumption condition, if the incident light projection of the detector D j is a non-vacuum state, D j must respond; if the incident light projection is a vacuum state, the probability of D j still responding is d j , that is, the dark count probability of the corresponding detector, and the probability of not responding at this time is 1-d jTherefore, if D1, D2 incident light is projected onto the state |s1s2>, it will be with a probability The event X i , Specifically as shown in Table I.

[0086] Table I

[0087]

[0088] Record The conditional probability of the quantum state of any photon number m produced by the beam splitter BS2 through the variable beam splitter VBS projected onto the quantum state |s1s2>, is Can be described as:

[0089]

[0090] Where the third beam splitter VBS produced by the transmitted light and reflected light are called the third transmitted light and the third reflected light, t v Indicates the beam splitting ratio of VBS, Indicates the probability of the u-th term in the binomial distribution; η1, η2 respectively represent the total efficiency of the third transmitted light and the third reflected light produced by the beam splitter VBS to reach the local single photon detector D1, D2, that is, the product of the beam coupling efficiency and the detection efficiency of the local single photon detector, Specifically as shown in Table II.

[0091] Table II

[0092]

[0093] Definition The probability of the event X i Occurring when the quantum state photon number is m, then:

[0094]

[0095] At this time, the Indicates the photon number distribution probability of the signal state when the event X i Occurs, where:

[0096]

[0097] Wherein, d1, d2 respectively represent the probability of D1, D2 response when the third transmitted light and the third reflected light generated by the beam splitter VBS project on the vacuum state respectively, t0 represents the splitting ratio of the beam splitter BS2, e is the natural constant, I represents the average photon number of the first transmitted light after the beam splitter BS1, that is, before entering the local detection response system, η1, η2 respectively represent the total efficiency of the third transmitted light and the third reflected light generated by the third beam splitter VBS to D1, D2.

[0098] Therefore, the four response events X1-X4 generated by the two single photon detectors of the sending end correspond to different event occurrence probabilities

[0099]

[0100]

[0101] Therefore, when Bob randomly selects a measurement basis to perform quantum state measurement, taking the Z basis measurement as an example, according to the four response events X1-X4 generated by the two single photon detectors of the sending end, which correspond to different H state detection response probabilities and V state detection response probabilities and further obtain the corresponding different system gains and system error numbers

[0102]

[0103] Wherein, p H represents the probability of triggering H state detector response when the sending end Alice sends a quantum state with polar angle θ and azimuth angle φ in the RL-Bloch sphere, and the receiving end Bob adopts Z basis measurement; p V represents the probability of triggering V state detector response when the sending end Alice sends a quantum state with polar angle θ and azimuth angle φ, and the receiving end Bob adopts Z basis measurement; d represents the probability of the receiving end Bob detector response when the transmission signal projects on the vacuum state; I represents the average photon number of the first transmitted light after the beam splitter BS1, that is, before entering the local detection response system; η represents the total efficiency of the quantum state sent by the sending end Alice and detected by the receiving end Bob, which is the product of the splitting ratio t0 of the beam splitter BS2, the channel transmission efficiency and the receiving end detection efficiency; i∈{1,2,3,4} is used to represent different events.

[0104]

[0105] Wherein, represents that any quantum state generated by the linear optical system is located in the post-selection region Ω kthe probability of the event X the probability of the event X respectively represent the system gain and the system error number of the non-normalized event X i the system gain and the system error number of the normalized event X the probability of the event X respectively represent the system gain and the system error number of the normalized event X i the system gain and the system error number of the normalized event X; the system error rate is equal to the ratio of the system error number to the system gain.

[0106] In addition, the system single-photon transmittance y1 can be obtained by using linear programming constraint conditions: min f=y1

[0107]

[0108]

[0109] 0≤y n ≤1 (n=1, 2, …, 9).

[0110] Similarly, the system single-photon error number e1 can be obtained by using linear programming constraint conditions:

[0111] max f=e1

[0112]

[0113] 0≤e n ≤1 (n=1, 2, …, 9).

[0114] wherein n represents the number of photons of a transmitted quantum state, y n represents the transmittance of the quantum state with the number of photons n, and e n represents the error number of the quantum state with the number of photons n.

[0115] In addition, the phase error rate under the X base in the full-passive quantum key distribution scheme is equal to the bit error rate under the Z base, and the probability of randomly selecting the Z base or the X base by the sender Alice is equal, and the system security key rate R is represented as:

[0116]

[0117] wherein, represents the probability of the signal state being a single-photon state when the event X i occurs, H2(x) is a binary Shannon entropy function, and satisfies H2(x)=-xlog2(x)-(1-x)log2(1-x); f EC represents the system error correction efficiency.

[0118] In this embodiment, the method of the present invention is verified through simulation experiments. The relevant system parameters are set as follows: fiber loss coefficient α = 0.2 dB / km, and Bob's detection efficiency at the receiving end is η. Bob =0.65, dark count rate d=10 -6 Furthermore, the dark count rate of Alice's local single-photon detection system at the transmitting end is d1 = d2 = 10. -6 The detection efficiency is η1 = η2 = 0.85, the beam splitting ratio of beam splitter BS2 is t0 = 0.01, and the beam splitting ratio of variable beam splitter VBS is t v =0.25.

[0119] The traditional quantum key distribution device used for comparison experiments in this embodiment distinguishes between signal states, decoy states, and vacuum states by accurately measuring the light intensity of the output quantum state. It does not include a local detection response module and calculates the secure key rate using the trace distance constraint method.

[0120] like Figure 2 The image shown is a simulation image of the secure key rate-distance between a conventional quantum key distribution device and the quantum key distribution device of this invention. Figure 2 It can be seen that the present invention can achieve 1.04 × 10 at a distance of 100 kilometers. -4 The secure bit / pulse generation rate can be achieved at 4.25 × 10^6 bits per second at a distance of 200 km. -7 The proposed scheme achieves a secure key generation rate of bits / pulses and enables quantum key distribution over distances exceeding 225 kilometers. The scheme in the literature achieves 9.01 × 10⁻⁶ at a distance of 100 kilometers. -5 A secure bit / pulse generation rate of 1.74 × 10⁻⁶ was achieved at 200 km. -7 The secure key generation rate per bit / pulse has a maximum transmission distance of 220 kilometers. This indicates that compared to the fully passive quantum key distribution schemes in previous literature, this invention can achieve a nearly 10% improvement in secure key rate over shorter transmission distances of less than 100 kilometers, and the improvement in secure key rate is even more significant over longer transmission distances, while also achieving a greater quantum key distribution distance.

Claims

1. A fully passive quantum key distribution apparatus, characterized by, The sending end comprises an arbitrary quantum state generating module and a local detection response module; The arbitrary quantum state generating module passively generates an arbitrary quantum coherent state on a Bloch sphere by using a linear optical system, first reflected light after the first beam splitter is used for polarization direction measurement and quantum state post-selection, and first transmitted light after the first beam splitter enters the local detection response module; In the local detection response module, second transmitted light after the second beam splitter enters a receiving end, second reflected light after the second beam splitter enters a third beam splitter, and two beams of light obtained after the third beam splitter enter two single-photon detectors respectively, and a photon number distribution model is established by using response and non-response events of the single-photon detectors; In the receiving end, two signals after the second polarization beam splitter enter an H state detector and a V state detector respectively, and a measurement result is obtained; a security key is obtained according to the polarization direction of the sending end, the photon number distribution model and the measurement result of the receiving end; In the arbitrary quantum state generating module, four incident lights with the same intensity and different random phases are input into the linear optical system, and first incident light and second incident light with orthogonal polarization states are obtained; the first incident light and the second incident light are input into the first beam splitter, the first incident light and the second incident light are taken as the north pole and the south pole of the Bloch sphere, an RL-Bloch sphere is obtained, and an arbitrary quantum coherent state with random phase, random intensity and random polarization direction in the RL-Bloch sphere is output, and the intensity and the polarization are coupled with each other; The photon number distribution model is established by using response and non-response events of the single-photon detectors, comprising: Two beams of light obtained after the third beam splitter enter a first single-photon detector and a second single-photon detector respectively, four response events are generated according to trigger results of the first single-photon detector and the second single-photon detector, and are denoted as X1-X4 respectively: X1: neither the first single-photon detector nor the second single-photon detector responds; X2: the first single-photon detector responds, and the second single-photon detector does not respond; X3: the second single-photon detector responds, and the first single-photon detector does not respond; X4: both the first single-photon detector and the second single-photon detector respond; Computing event X i Transmission signal transmitted to a receiving end at the time of occurrence Density matrix projected into the photon number space.

2. The fully passive quantum key distribution apparatus according to claim 1, wherein The probability density functions of the phase, the intensity and the polarization direction of the quantum coherent state satisfy: where υ denotes the average light intensity of the incident light, t denotes the splitting ratio of the first beam splitter, and φ ∈ (-π, π], θ ∈ [0, π], I ∈ [0, I max,θ ), φ denotes the azimuth angle of the RL-Bloch sphere, θ denotes the polar angle of the RL-Bloch sphere, I denotes the average number of photons of the first transmitted light after the first beam splitter, f θ,I (θ, I) denotes the joint probability density function of the quantum state polar angle and the average light intensity.

3. The fully passive quantum key distribution apparatus according to claim 2, wherein, The transmitting end and the receiving end agree that the linear polarization direction 0, π in the RL-Bloch sphere constitutes the Z basis, and the linear polarization direction constitutes the X basis; The sending end determines an acceptable polar angle variation Δθ and an acceptable azimuth angle variation Δφ according to a distance between the sending end and the receiving end, performs quantum state post-selection, and the quantum state after the post-selection is: where r represents the Fock state photon number, and k represents the linear polarization direction of the quantum state, i.e.

4. The fully passive quantum key distribution apparatus according to claim 1, wherein After the sending end performs quantum state post-selection, a group of quantum state random key sequences and a group of corresponding base selection sequences are obtained, the random key sequences are sent to the receiving end, and the base selection sequences are published; The receiving end selects a random sequence to determine a measurement base, and obtains a measurement result sequence; the receiving end compares the base selection sequence and the measurement result sequence, and obtains a security key.

5. The fully passive quantum key distribution apparatus according to claim 1, wherein, The third beam splitter is a variable beam splitter.

6. A method for all-passive quantum key distribution based on the apparatus of claim 1, characterized in that, The method comprises the following steps: The arbitrary quantum state of the sending end is generated by a linear optical system to generate an arbitrary quantum coherent state on a Bloch sphere by a generating module, first reflected light after a first beam splitter is used for polarization direction measurement and quantum state post-selection, and first transmitted light after the first beam splitter enters the local probe response module; In the local probe response module, second transmitted light after the first transmitted light passing through a second beam splitter enters a receiving end, second reflected light after the second beam splitter enters a third beam splitter, and two beams of light obtained after the third beam splitter enter two single-photon detectors respectively, and a corresponding photon number distribution model is established by using response and non-response events of the single-photon detectors; In the receiving end, two-way signals after the second transmitted light passing through a second polarization beam splitter enter an H state detector and a V state detector respectively, and measurement results are obtained; and a security key is obtained according to the polarization direction of the sending end, the photon number distribution model and the measurement results of the receiving end.

7. A method for estimating the key rate of a fully passive quantum key distribution apparatus according to any one of claims 1 to 5, characterized by, The system security key rate R is: where, represents event X i , H2(x) is the binary Shannon entropy function; f EC represents the system error correction efficiency, e1 is the single photon error code number, y1 is the single photon transmittance, and respectively represent the system gain and the system error code number of event X i , is the probability that the arbitrary quantum state generated by the linear optical system is located in the post-selection region Ω k .

8. The key rate estimation method of claim 7, wherein, The single-photon transmittance is calculated by solving a linear programming problem: min f=y1 s.t. 0 ≤ y n ≤ 1 (n = 1, 2,..., 9) The single-photon error code number is calculated by solving a linear programming problem: max f=e1 s.t. 0 ≤ e n ≤ 1 (n = 1, 2,..., 9) where n represents the number of photons of the transmitted quantum state, y n represents the transmission rate of a quantum state with n photons, e n represents the number of errors of a quantum state with n photons.

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