CN109525326B - Quantum key distribution method based on single-photon ultra-dense coding - Google Patents
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Abstract
The invention discloses a quantum key distribution method based on single-photon ultra-dense coding, which comprises the steps that a party A prepares a photon state which is randomly in an R ground state, the photon state is sent to a party B after deflection operation is carried out, the party B returns to the party A after deflection operation is carried out again, the party A compares the quantum state obtained by measurement with the originally prepared quantum state, a comparison result is sent to the party B, the party A judges whether a used measurement base is correct or not, if the used measurement base is correct, marking is carried out, then marked position information is sent to the party B, wrong position information is discarded, and finally the party A and the party B generate a shared bit string according to own information and received information. Compared with the entangled-state QDKD protocol, the method provided by the invention does not need complex quantum resources and equipment, and is more economical and feasible.
Description
Technical Field
The invention discloses a quantum key distribution method based on single-photon ultra-dense coding, and belongs to the technical field of quantum secret communication.
Background
With the application of quantum mechanical theory in the field of information processing, quantum secret communication is used to accomplish many interesting tasks, such as Quantum Key Distribution (QKD), Quantum Secret Sharing (QSS), Quantum Key Agreement (QKA), and the like. With QKD being the most basic and important direction of research for generating private keys between two legitimate users, by means of which both users can securely communicate their secret messages. In general, these QKD protocols can be divided into two categories: single-photon based QKD protocols such as BB84 and E92; the other is the entangled state based QKD protocol. In the two categories, the single-photon QKD protocol is simple and feasible in experiment but low in efficiency; the entangled-state QKD protocol is more efficient but requires more complex quantum resources and devices.
The QKD protocol requires key distribution efficiency to be considered in addition to ensuring security. In 2004, degiovenni et al proposed a new protocol that combines quantum super-dense encoding and quantum key distribution, called quantum super-dense key distribution (QDKD) protocol, which embeds key information by manipulation on entangled pairs (i.e., Bell states), with better key generation rate than BB84 protocol. The QDKD protocol proposed by Degiovanni et al has been shown to be secure and able to detect any single eavesdropping attack. The concept of the QDKD protocol is widely used, and other scholars successfully apply the concept to different entangled-state QKD protocols. For example, in 2011, Hwang et al proposed the QKD protocol by dense encoding with three qubit W-states. In 2013, liu shihao et al proposed a quantum simultaneous secret allocation protocol that was densely coded on the cluster state. However, these protocols are based on entangled QKD protocols, and therefore have a problem that complicated quantum resources and devices are required.
Disclosure of Invention
The invention aims to overcome the defects that complex quantum resources and equipment are needed for entangled-state QKD and the like, and provides an economical and feasible quantum key distribution method based on single-photon ultra-dense coding.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a quantum key distribution method based on single-photon ultra-dense coding comprises the following steps:
1) a, preparing a single photon state | Ψ >, | Ψ > being randomly in an R ground state; then, A deflects the photon state with a certain probability and sends to B;
2) b, receiving the photons sent by A, and enabling the photons to be in an R ground state or a D ground state with different probabilities; then B deflects the photon state with a certain probability and returns to A;
3) a receives photons sent by B and is in an R ground state or a D ground state with different probabilities; then measuring the A to obtain a photon state | Ψ' >;
4) a, comparing | Ψ' > with | Ψ >, and sending comparison result information to B through a typical channel;
5) b informs A of deflection operation information of the B in the step 2) by using a classical channel;
6) a judges whether the used measuring base is correct according to the received information, if so, the measuring base is marked as Y, otherwise, the measuring base is marked as N, and then the position information marked as Y or N is sent to B;
7) b, discarding all information marked as N according to the position information sent by A;
8) a and B generate a shared bit string from their own information and the received information.
The foregoing R ground state is |0>Or |1>The D ground state is
Or
In the foregoing step 1) and step 2), the operation of deflecting the photon state with a certain probability means that U is used with a probability of (1-P)/200Deflecting the photon state, or using U with P/2 probability01Deflecting the photon state, or using U with a probability of (1-P)/210Deflecting the photon state, or using U with P/2 probability11Deflecting the photon state, wherein U00、U01、U10、U11Respectively deflect 0 degrees, 45 degrees, 90 degrees and 135 degrees,
in the aforementioned step 3), A measures photons using the R basis with a (1-P) probability, or using the D basis with a P probability.
In the foregoing step 4), the result information sent by a is: if | Ψ' > - | Ψ > - |0>, then "00" is transmitted; if | Ψ' > - | Ψ > - | + >, send "01"; if | Ψ' > - | Ψ > - |1>, sending "10"; if | Ψ' > - | Ψ > - | >, an "11" is sent.
In the aforementioned step 5), if B deflects the photon state by 0 ° or 90 ° in said step 2), then "0" is sent; if the deflection is 45 or 135, a "1" is sent.
Compared with the prior art, the invention has the following advantages:
1. compared with the single-photon QKD protocol, the invention has high coding capacity, and each related photon can carry two bits of useful information.
2. Compared with the entangled-state QDKD protocol, the method provided by the invention does not need complex quantum resources and equipment, and is more economical and feasible.
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FIG. 1 is a process diagram of a quantum key distribution method based on single-photon ultra-dense coding according to the present invention.
Fig. 2 is a quantum key distribution example based on single-photon ultra-dense coding according to the invention.
Detailed Description
The invention is further described below. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
As shown in fig. 1, the quantum key distribution process based on single photon super-dense coding is divided into four columns, each column indicating a host, a photon state and an operation to be performed. The invention discloses a quantum key distribution method based on single-photon ultra-dense coding, which comprises the following steps of:
1) as shown in the first column, user Alice prepares a single photon state | Ψ >, | Ψ > being randomly placed in either |0> or |1>, i.e., the R ground state. In the actual operation process, the method of the invention is executed for multiple times, so as to realize the length of the bit string which meets the requirement of sharing.
Then, Alice uses U with a probability of (1-P)/200To | Ψ>Performing a deflecting operation, or using U with a probability of P/201To | Ψ>Performing a deflection operation or using U with a probability of (1-P)/210To | Ψ>Performing a deflecting operation, or using U with a probability of P/211To | Ψ>And performing deflection operation and sending the deflection operation to the user Bob. U shape00、U01、U10、U11Respectively 0 degrees, 45 degrees, 90 degrees, 135 degrees of deflection, wherein,
2) as shown in the second column, photons received by Bob are in the R ground state { |0 with different probabilities>，|1>Either the D ground state
E.g. performing U on R ground state00Or U10Deflecting to obtain R ground state, and subjecting the R ground state to U01Or U11And deflecting to obtain the D ground state.
Then Bob was treated with a molar ratio of (1-P)/2, P/2, (1-P)/2,
probability of using U00、U01、U10、U11The photons are deflected and then returned to Alice.
3) As shown in the third column, photons received by Alice are in the R and D ground states with different probabilities. E.g. performing U on R ground state00Or U10Deflecting to obtain R ground state, and subjecting the R ground state to U01Or U11Deflecting to obtain D ground state, and subjecting the D ground state to U00Or U10Deflecting to obtain D ground state, and subjecting the D ground state to U01Or U11The operation of the deflection is carried out,the R ground state is obtained.
Alice then measures the photon using the R-basis with a (1-P) probability, or using the D-basis with a P probability, resulting in state | Ψ' >.
Then, Alice transmits the result information to Bob through a classical channel, and if | Ψ' > - | Ψ > - |0>, transmits "00"; if | Ψ' > - | Ψ > - | + >, send "01"; if | Ψ' > - | Ψ > - |1>, sending "10"; if | Ψ' > - | Ψ > - | >, an "11" is sent.
4) Bob informs Alice of the operation information using the classical channel, and if Bob deflects photons by 0 ° or 90 ° in step 2), transmits "0"; if the deflection is 45 or 135, a "1" is sent.
5) And according to the received information, the Alice judges whether the used measurement base is correct, if so, the measurement base is marked as Y, otherwise, the measurement base is marked as N, and then the position information marked as Y and N is sent to the Bob. A position is a bit sequence position.
6) And according to the position information sent by Alice, all the information marked as N is discarded by Bob.
7) And generating a shared bit string by Alice and Bob according to the self information and the received information, wherein the shared bit string is generated by the deflection operation executed by Alice and Bob.
Taking an 8-bit qubit as an example, the qubit number should be such that the resulting shared bit string satisfies the required length. Fig. 2 describes a shared bit string generation process in the quantum key distribution protocol based on single-photon ultra-dense coding according to the present invention. As shown in the first-bit qubit of FIG. 2, assuming the initial quantum state is |0>, one possible implementation is as follows:
11) alice prepares the photon to be in the quantum state | Ψ>，|Ψ>At |0>Then Alice pairs |0>To carry out U10Operated on to obtain a quantum state of |1>And the photons are transmitted to Bob through a quantum channel.
12) Bob receives photons, but does not measure them, but rather performs U on them11Operated to give | Ψ'>And then sends the photons back to Alice.
13) Alice receives the photon, measures the photon with the D base according to the probability of P, and the state is | Ψ' >, through measurement. After the measurement, Alice announces "01" and transmits the information to Bob because | Ψ' > - | Ψ > - | + > - |0> - | + >.
14) Bob sends Alice information of the operation performed on the photons using the classical channel, Bob deflects the photons by 135 °, so that a "1" is transmitted to Alice.
15) Alice determines from the received information that the measurement base used is correct, retains this bit and marks it as Y, and then sends the retained or discarded information to Bob.
16) Bob selects the reservation based on the location information sent by Alice.
17) Alice knows that he operates on photons as U10And according to the public information, the operation of the photon by Bob can be deduced to be U11. Also, Bob knows that he operates on photons as U itself11According to the public information, the operation of Alice on the photon can be deduced to be U10. Finally, Alice and Bob may share information bits "1011," where "10" is the result of the operation used by Alice and "11" is the result of the operation used by Bob.
As shown in the second bit qubit of fig. 2, some possible implementation is as follows:
21) alice prepares the photon to be in the quantum state | Ψ>，|Ψ>At |0>Then Alice pairs |0>To carry out U11Operating to obtain quantum state | ->And the photons are transmitted to Bob through a quantum channel.
22) Bob receives photons, but does not measure them, but rather performs U on them00Operated to give | Ψ'>And then sends the photons back to Alice.
23) Alice receives the photon, measures the photon with the R-base at a probability of (1-P), and measures the state | Ψ' >. After the measurement, Alice declares "11" because | Ψ' > - | Ψ > - |0> - | >, and transmits the information to Bob.
24) Bob sends Alice information of the operation performed on the photons using the classical channel, Bob deflects the photons by 0 °, so that "0" is transmitted to Alice.
25) Alice determines from the received information that the measurement base used is erroneous, discards this bit and marks it as N, and then sends the retained or discarded information to Bob.
26) And Bob selects to discard according to the position information sent by Alice.
A similar procedure is performed for the remaining 6 single photons to obtain the key string "101100000001110101001000".
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (4)
1. A quantum key distribution method based on single-photon ultra-dense coding is characterized by comprising the following steps:
1) a preparation of Single photon state | Ψ>，|Ψ>Randomly in an R ground state; then, A pairs the single photon state | Ψ with a certain probability>Performing deflection operation and sending the deflection operation to B; the method comprises the following steps: a uses U with a probability of (1-P)/200To | Ψ>Performing a deflection operation, or A using U with a probability of P/201To | Ψ>Performing a deflection operation, or A using U with a probability of (1-P)/210To | Ψ>Performing a deflection operation, or A using U with a probability of P/211To | Ψ>Performing a deflection operation in which U00、U01、U10、U11Respectively deflect 0 degrees, 45 degrees, 90 degrees and 135 degrees,
2) b, receiving the photons sent by A, and enabling the photons to be in an R ground state or a D ground state with different probabilities; then B deflects the photon state with a certain probability and returns to A; the method comprises the following steps: b uses U with the probability of (1-P)/2, P/2, (1-P)/2, P/2 respectively00、U01、U10、U11Deflecting the photons;
3) a receives photons sent by B and is in an R ground state or a D ground state with different probabilities; then measuring the A to obtain a photon state | Ψ' >; the method comprises the following steps: a measures photons using the R-basis with a (1-P) probability, or the D-basis with a P probability, resulting in a photon state | Ψ' >;
4) a, comparing | Ψ' > with | Ψ >, and sending comparison result information to B through a typical channel;
5) b informs A of deflection operation information of the B in the step 2) by using a classical channel;
6) a, judging whether the used measurement base is correct or not according to the received information, if so, marking as Y, otherwise, marking as N, and then sending the position information marked as Y and N to B;
7) b, discarding all information marked as N according to the position information sent by A;
8) a and B generate a shared bit string according to own information and received information; the shared bit string is generated by the deflection operations performed by a and B.
2. The quantum key distribution method based on single photon ultra-dense coding according to claim 1, wherein the R ground state is |0>Or |1>The D ground state is
Or
3. The quantum key distribution method based on single photon ultra-dense coding according to claim 1, wherein in the step 4), the result information sent by A is: if | Ψ' > - | Ψ > - |0>, then "00" is transmitted; if | Ψ' > - | Ψ > - | + >, send "01"; if | Ψ' > - | Ψ > - |1>, sending "10"; if | Ψ' > - | Ψ > - | >, an "11" is sent.
4. The method for distributing quantum keys based on single photon ultra-dense coding according to claim 1, wherein in the step 5), if B deflects photon state by 0 ° or 90 ° in the step 2), then "0" is sent; if the deflection is 45 or 135, a "1" is sent.
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