CN114401088A - Quantum secret sharing method based on super-entanglement assistance - Google Patents

Quantum secret sharing method based on super-entanglement assistance Download PDF

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CN114401088A
CN114401088A CN202210110890.6A CN202210110890A CN114401088A CN 114401088 A CN114401088 A CN 114401088A CN 202210110890 A CN202210110890 A CN 202210110890A CN 114401088 A CN114401088 A CN 114401088A
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CN114401088B (en
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周澜
居星星
薛智文
盛宇波
钟伟
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Nanjing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography
    • H04L9/0858—Details about key distillation or coding, e.g. reconciliation, error correction, privacy amplification, polarisation coding or phase coding
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/70—Photonic quantum communication
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/80—Optical aspects relating to the use of optical transmission for specific applications, not provided for in groups H04B10/03 - H04B10/70, e.g. optical power feeding or optical transmission through water
    • H04B10/85—Protection from unauthorised access, e.g. eavesdrop protection
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
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Abstract

A quantum secret sharing method based on super-entanglement assistance is characterized in that a user 1 prepares a super-entangled three-photon GHZ state and selects a security detection photon pair. User 1 sends two photons in all super-entangled GHZ states to user 2 and user 3. After receiving the photons, user 1 publishes the location and measurement base for security detection photons; and (3) carrying out coding operation on the non-safety detected photon pair, the user 2 and the user 3, and carrying out complete GHZ state analysis of polarization freedom by the three-party user. The user 1 obtains the encoded polarization GHZ state to obtain an original key; for the photon pair for safety detection, the three users use the measuring base to measure the photons in the hands of the three users, the safety detection is carried out, and if the photons pass through the measuring base, the three users carry out error correction and secret amplification on the original secret key to form a final safety secret key. In the method, the complete distinction of eight polarization GHZ states is realized without base processing, each super-entangled GHZ state can transmit a 3-bit key, the key generation efficiency is obviously improved, and the practicability is improved.

Description

Quantum secret sharing method based on super-entanglement assistance
Technical Field
The invention belongs to the technical field of quantum communication, and particularly relates to a quantum secret sharing method based on super-entanglement assistance.
Background
Quantum communication is a method of transferring information by using the basic principle of quantum mechanics. The safety of quantum communication is based on the basic principles of quantum mechanics, including the unclonable theorem, entangled non-localization property and the like. The eavesdropping behavior of any eavesdropper will corrupt the state of the transmitted particles and thus be discovered by the communicating party. Therefore, quantum communication has absolute security, which is the greatest advantage of quantum communication from classical communication.
Quantum cryptography is an important branch of quantum communication and mainly includes Quantum Key Distribution (QKD), Quantum Secret Sharing (QSS), and the like. QKD refers to the distribution of a secure key between two users using an entangled channel. QSS means that a secret sender splits secret information into a plurality of partial sub-passwords and distributes the partial sub-passwords to a plurality of agent members by taking quantum states as carriers; only the agent members collaborate together can the secret be recovered. Similarly, the QSS also allows multiple agent members to collectively deliver a key to a receiver through collaboration. Like QKD, QSS has unconditional security in theory and has important application values in national defense, finance and other aspects. The original QSS scheme requires the distribution of the GHZ state among three communicating parties, who randomly pick either a right-base or a diagonal-base opponent for photon measurements. Only when the measurement bases selected by three parties are the same, the key transmission can be realized, and the traditional GHZ state analysis can only distinguish 2 of 8 GHZ states, which results in lower key generation rate of the original QSS.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a quantum secret sharing method based on super-entanglement assistance, wherein a user 2 and a user 3 jointly transfer a secret key to a user 1 through cooperation. The method does not need three communication parties to carry out base processing, and can completely distinguish eight GHZ states by utilizing linear optics, so that the generation rate of the security key of the QSS can be obviously improved, and the method can be completely realized under the current experimental condition.
A quantum secret sharing method based on super-entanglement assistance comprises the following steps:
step 1, a user 1 uses a super-entanglement source to prepare a large number of same polarized P-momentum M super-entangled three-photon GHZ states for quantum communication; the user 1 splits each super-entangled photon pair into three photon sequences, which are named as sequences 1,2 and 3 respectively; meanwhile, the user 1 randomly selects a three-photon GHZ state as a safety detection photon pair;
step 2, the user 1 sends the photons of the sequence 2 and the sequence 3 to the user 2 and the user 3 respectively, the user 2 and the user 3 inform the user 1 through classical communication after receiving the photons, the user 1 publishes the positions of all the safety detection photon pairs and publishes measurement bases of two degrees of freedom, and the measurement bases randomly select one from a right-angle base and a diagonal base;
step 3, for the non-safety detection photons in the sequence 2 and the sequence 3, the user 2 and the user 3 respectively use the unitary operation on 4 polarization degrees of freedom at random, and carry out coding operation on the polarization degrees of freedom to load a key, but do not carry out any operation on the momentum degree of freedom;
step 4, after the coding is finished, the user 1, the user 2 and the user 3 utilize momentum freedom entanglement as assistance to carry out complete GHZ state analysis of polarization freedom on the coded three-photon pair; the user 2 and the user 3 publish respective detector response conditions, and the user 1 knows the encoded GHZ state by combining the own detector response conditions, so that a key jointly transmitted by the user 2 and the user 3 is obtained;
step 5, for the safety detection photon pair, the user 1, the user 2 and the user 3 measure the two degrees of freedom of polarization and momentum according to the published measuring base of the user 1 and publish the measuring result; in any degree of freedom, if the measurement basis is a right-angle basis, the three-party measurement results are used for estimating the bit error rate in the photon transmission process; if the measurement basis is a diagonal basis, the measurement results of the three parties are used for estimating the phase error rate in the photon transmission process; the sum of the two error rates is defined as the total error rate in the degree of freedom; if the total error rate of the safety detection photons in any degree of freedom exceeds a set threshold value, the transmission process of the photons is proved to be unsafe, communication is stopped, and the original secret key is discarded by a user; if the total error rate of the two degrees of freedom is lower than a set threshold value, the photon transmission process is proved to be safe, and the next step is carried out;
and 6, carrying out error correction and private amplification on the public channel by the user 1, the user 2 and the user 3 to form a final security key.
Further, the user 1 uses the super-entanglement source to prepare the polarization-momentum super-entangled GHZ state
Figure BDA0003495034600000031
Wherein, | ψ1 +>PBelonging to one of 8 polarized GHZ states, and the expressions of the 8 polarized GHZ states under the Z group and the X group are respectively as follows:
Figure BDA0003495034600000032
Figure BDA0003495034600000033
Figure BDA0003495034600000041
Figure BDA0003495034600000042
Figure BDA0003495034600000043
Figure BDA0003495034600000044
Figure BDA0003495034600000045
Figure BDA0003495034600000046
|H>、|V>is the basis vector of Z group, respectively represents the horizontal polarization and the vertical polarization of photons, | +/->PIs the basis vector of the X group,
Figure BDA0003495034600000047
subscripts 1,2,3 represent the serial number of the photon;
|ψ1 +>M8 GHZ states belonging to momentum freedom, the form of the 8 momentum GHZ states under Z group and X group is:
Figure BDA0003495034600000051
Figure BDA0003495034600000052
Figure BDA0003495034600000053
Figure BDA0003495034600000054
Figure BDA0003495034600000055
Figure BDA0003495034600000056
Figure BDA0003495034600000057
Figure BDA0003495034600000061
wherein, | L>，|R>Is the basis vector of the Z group and respectively represents the left and right of momentum, | +/->MIs a basis vector of a diagonal basis, satisfies
Figure BDA0003495034600000062
Subscripts 1,2,3 represent the sequence number of the photon, respectively.
Further, in step 3, for the three-party shared non-security detection of the super-entangled GHZ photon pair, the user 2 and the user 3 do nothing to the photon in the momentum degree of freedom, and perform the encoding operation in the polarization degree of freedom, and the four encoding operations in the polarization degree of freedom include:
Figure BDA0003495034600000063
Figure BDA0003495034600000064
Figure BDA0003495034600000065
Figure BDA0003495034600000066
after the coding is completed, the polarization GHZ state shared by the three-party users evolves to | psii ±>P(i ═ 1,2,3, 4); three-party users agree on | psi in advance1 +>P、|ψ1 ->P、|ψ2 +>P、|ψ2 ->P、|ψ3 +>P、|ψ3 ->P、|ψ4 +>P、|ψ4 ->PRepresenting 8 codes of 000, 001, 010, 011, 100, 101, 110, 111, respectively.
Further, in step 4, the user 1, the user 2 and the user 3 realize complete GHZ state analysis of polarization freedom degree through momentum entanglement assistance, that is, 8 polarization GHZ states can be completely distinguished; three user places respectively have 4 single photon detectors, are user 1 respectively:
Figure BDA0003495034600000067
and (4) a user 2:
Figure BDA0003495034600000068
user 3:
Figure BDA0003495034600000069
each GHZ state corresponds to 8 different detector response conditions with equal probability; users 2 and 3 publish the single photon detector response conditions at the positions, and the user 1 combines the detector response conditions to estimate the encoded GHZ state
Figure BDA0003495034600000071
Thereby inferring the original key that user 2 and user 3 jointly delivered.
Further, in step 5, the security detection includes:
user 1 publishes the location and measurement basis of the security detection photon pairs, and then the three users randomly select either the Z-basis or X-basis to measure the security detection photons in the pairs and publish the measurement results. In the degree of freedom of polarization and momentum, if the measurement base is a rectangular base, the three-party measurement result is used for estimating the bit error rate Q of the photon transmission processPb(QMb)，QPb(QMb) A probability that the three-way measurements are not all the same; if the measurement basis is a diagonal basis, the three-party measurement result is used for estimating the phase error rate Q of the photon transmission processPp(QMp)，QPp(QMp) The measurement result equal to three parties has even number | +>P(M)The probability of (d); the sum of the two error rates is defined as the total error rate Q in this degree of freedomPt＝QPb+QPp(QMt＝QMb+QMp) (ii) a If QPtOr QMtIf the value is higher than the set threshold value, indicating that the photon transmission process is unsafe, discarding the generated original secret key, and rechecking the channel; total error rate Q when two degrees of freedomPtAnd QMtAnd when the values are all lower than the set threshold value, the communication safety is indicated.
Further, in the method, the initial quantum state of the super-entangled photons and the coded detector response conditions of the users 2 and 3 are public information, the detector response condition of the user 1 is not public, and the polarization GHZ state shared by the users 2 and 3 after the coding is completed is only known by the user 1.
Further, the method has a secure key generation rate RsecThe expression is as follows:
Rsec＝Rsift[1-(1+f)H(Qt)]
wherein Q istRepresenting the total error rate, R, of the keysiftRepresenting the generation rate of the screening key, f is the error correction efficiency of the post-processing, f is 1.16, and h (x) is binary shannon entropy:
H(x)＝-x log2(x)-(1-x)log2(1-x).
the total error rate of the key is Qt＝(1-QPt)(1-QMt)。
Compared with the prior art, the invention has the following beneficial effects:
(1) the method prepares GHZ state super-entangled photon pairs for quantum communication in advance, and the user 1 sends two photons in each GHZ state photon pair to the user 2 and the user 3 respectively. After the distribution of photons is finished, security detection is adopted, so that an eavesdropper cannot intercept the photons and cannot find the photons, key leakage can be eliminated theoretically, and the security of a key transmission process is ensured.
(2) The method uses the polarization-momentum super-entangled GHZ state and utilizes momentum entanglement assistance to realize complete polarization GHZ state analysis, so that three-party users can generate the secret key without performing base operation. Because the polarization GHZ state analysis scheme can completely distinguish 8 polarization GHZ states, theoretically, each pair of super-entangled GHZ states can transmit a 3-bit key, and the key transmission efficiency of the QSS can be obviously improved.
(3) All equipment used by the method is based on linear optics and can be realized under the existing experimental conditions, and the practicability of the scheme is improved.
Drawings
Fig. 1 is a flowchart of a quantum secret sharing method based on super-entanglement assist in an embodiment of the present invention.
Fig. 2 is a diagram of analyzing a super-entangled GHZ state based on a super-entanglement assisted quantum secret sharing method in an embodiment of the present invention, wherein a PBS represents a polarization beam splitter, and is capable of completely transmitting H-polarized photons and completely reflecting V-polarized photons. HWP stands for half-wave plate and can be realized
Figure BDA0003495034600000081
Figure BDA0003495034600000082
Representing 12 single photon detectors.
FIG. 3 is a functional block diagram of a quantum secret sharing method based on super-entanglement assistance in an embodiment of the invention; encode stands for user 2 and user 3 encoders, and can perform four encoding operations on photons in polarization freedom.
Fig. 4 is a diagram of a detector response situation and a corresponding situation of a polarized GHZ state of a quantum secret sharing method based on super-entanglement assistance in an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings in the specification.
As shown in fig. 1, an embodiment of the present invention provides a quantum secret sharing method based on super-entanglement assist, including:
step 1: user 1 uses a super-entanglement source to prepare a large number of identical polarization (P) -momentum (M) super-entangled three-photon GHZ states for quantum communication. User 1 splits each super-entangled photon pair into three photon sequences, named separatelyIs sequence 1,2, 3. The super-entangled three-photon GHZ state form is
Figure BDA0003495034600000091
Wherein, | ψ1 +>PBelongs to one of 8 polarized GHZ states, and under the Z group and the X group, the expressions of the 8 polarized GHZ states are respectively as follows:
Figure BDA0003495034600000092
Figure BDA0003495034600000093
Figure BDA0003495034600000101
Figure BDA0003495034600000102
Figure BDA0003495034600000103
Figure BDA0003495034600000104
Figure BDA0003495034600000105
Figure BDA0003495034600000106
|H>、|V>is the basis vector of Z group, respectively represents the horizontal polarization and the vertical polarization of photons, | +/->PIs the basis vector of the X group,
Figure BDA0003495034600000107
subscripts 1,2, and 3 represent the sequence number of the photon.
Similarly, | ψ1 +>M8 GHZ states belonging to momentum freedom, and under the Z group and the X group, the forms of the 8 momentum GHZ states are as follows:
Figure BDA0003495034600000111
Figure BDA0003495034600000112
Figure BDA0003495034600000113
Figure BDA0003495034600000114
Figure BDA0003495034600000115
Figure BDA0003495034600000116
Figure BDA0003495034600000117
Figure BDA0003495034600000121
wherein, | L>、|R>Is the basis vector of the Z group and respectively represents the left and right of momentum, | +/->MIs a basis vector of a diagonal basis, satisfies
Figure BDA0003495034600000122
Subscripts 1,2, and 3 represent the sequence number of the photon.
At the same time, user 1 randomly selects a sufficient number of three-photon GHZ states as security detection photon pairs. The user 1 sends the photons of the sequence 2 and the sequence 3 to the user 2 and the user 3 respectively, after the user 2 and the user 3 receive the photons, the user 1 is informed, and the user 1 publishes the position of the security detection photon pair and a measuring base of two degrees of freedom (randomly selected from a right angle base and a diagonal base).
For a three-party shared non-safety detection super-entangled GHZ photon pair, the photons of the users 2 and 3 are encoded in the polarization degree of freedom without any operation on the momentum degree of freedom. The four encoding operations in polarization degrees of freedom include:
Figure BDA0003495034600000123
Figure BDA0003495034600000124
Figure BDA0003495034600000125
Figure BDA0003495034600000126
the above operation can make GHZ state | ψ in the polarization degree of freedom1 +>PThe evolution was to the 8 polarized GHZ states mentioned above. For example, if the user 2 operates as
Figure BDA0003495034600000127
The operation of the user 3 is
Figure BDA0003495034600000128
GHZ state in polarization degree of freedom will evolveInto
Figure BDA0003495034600000129
Three users agree on a good | ψ1 +>P，|ψ1 ->P，|ψ2 +>P，|ψ2 ->P，|ψ3 +>P，|ψ3 ->P，|ψ4 +>P，|ψ4 ->PRepresenting 8 encodings (original keys) of 000, 001, 010, 011, 100, 101, 110, 111, respectively.
After the coding is completed, the user 1, the user 2 and the user 3 utilize momentum entanglement to assist in realizing complete GHZ state analysis of the polarization degree of freedom, namely, 8 polarization GHZ states can be completely distinguished. Three user places respectively have 4 single photon detectors, are user 1 respectively:
Figure BDA0003495034600000131
and (4) a user 2:
Figure BDA0003495034600000132
user 3:
Figure BDA0003495034600000133
each polarization GHZ state corresponds to 8 different detector response conditions with equal probability, and the specific detector response conditions corresponding to 8 polarization GHZ states are shown in fig. 4.
After the measurement is finished, the user 2 and the user 3 publish the response condition of the single photon detector at the position, and the user 1 estimates the coded super-entangled GHZ state according to the response condition of the three-party detector
Figure BDA0003495034600000134
Thereby obtaining the key jointly delivered by the user 2 and the user 3. For example, if the user 2 operates as
Figure BDA0003495034600000135
The operation of the user 3 is
Figure BDA0003495034600000136
E.g. the encoded polarization GHZ state is | ψ4 ->PUser 1 can obtain the key 111 jointly transmitted by user 2 and user 3, if the operation of user 2 is
Figure BDA0003495034600000137
The operation of the user 3 is
Figure BDA0003495034600000138
E.g. the encoded polarized GHZ state is
Figure BDA0003495034600000139
Figure BDA00034950346000001310
User 1 may obtain a key of 011 for the combined delivery of user 2 and user 3.
In order to ensure the security of the key transmission process, three users need to perform security detection. For the security detection photon pair, user 1, user 2 and user 3 measure them in two degrees of freedom, polarization and momentum, according to the published measurement bases, and publish the measurement results. In any degree of freedom, if a right-angle basis is selected, the three-party measurement results can be used for estimating the bit error rate in the photon transmission process; if a diagonal basis is chosen, the three-way measurements can be used to estimate the phase error rate of the photon transmission process. The sum of the two error rates is defined as the total error rate in that degree of freedom. If the total error rate of the safety detection photons in any degree of freedom exceeds a set threshold value, the transmission process of the photons is proved to be unsafe, communication is stopped, and the original secret key is discarded by a user; if the total error rate of the two degrees of freedom is lower than the set threshold value, the photon transmission process is proved to be safe, and the original secret key is reserved by the user.
Finally, user 1, user 2 and user 3 perform error correction and privacy amplification on the public channel to form the final security key.
It should be noted that an eavesdropper cannot acquire information during communication. During the transmission process in which the user 1 transmits photons to the users 2 and 3, no encoding operation is performed at this time, so that the transmitted photons do not contain key information, i.e., no information can be obtained by an eavesdropper. After encoding, only the user 2 and the user 3 publish the measurement results, and the user 1 does not publish the measurement results publicly, so that an eavesdropper cannot obtain encoded GHZ state information, and the whole scheme can be ensured to be safe.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.

Claims (7)

1. A quantum secret sharing method based on super-entanglement assistance is characterized in that: the method comprises the following steps:
step 1, a user 1 uses a super-entanglement source to prepare a large number of same polarized P-momentum M super-entangled three-photon GHZ states for quantum communication; the user 1 splits each super-entangled photon pair into three photon sequences, which are named as sequences 1,2 and 3 respectively; meanwhile, the user 1 randomly selects a three-photon GHZ state as a safety detection photon pair;
step 2, the user 1 sends the photons of the sequence 2 and the sequence 3 to the user 2 and the user 3 respectively, the user 2 and the user 3 inform the user 1 through classical communication after receiving the photons, the user 1 publishes the positions of all the safety detection photon pairs and publishes measurement bases of two degrees of freedom, and the measurement bases randomly select one from a right-angle base and a diagonal base;
step 3, for the non-safety detection photons in the sequence 2 and the sequence 3, the user 2 and the user 3 respectively use the unitary operation on 4 polarization degrees of freedom at random, and carry out coding operation on the polarization degrees of freedom to load a key, but do not carry out any operation on the momentum degree of freedom;
step 4, after the coding is finished, the user 1, the user 2 and the user 3 utilize momentum freedom entanglement as assistance to carry out complete GHZ state analysis of polarization freedom on the coded three-photon pair; the user 2 and the user 3 publish respective detector response conditions, and the user 1 knows the encoded GHZ state by combining the own detector response conditions, so that a key jointly transmitted by the user 2 and the user 3 is obtained;
step 5, for the safety detection photon pair, the user 1, the user 2 and the user 3 measure the two degrees of freedom of polarization and momentum according to the published measuring base of the user 1 and publish the measuring result; in any degree of freedom, if the measurement basis is a right-angle basis, the three-party measurement results are used for estimating the bit error rate in the photon transmission process; if the measurement basis is a diagonal basis, the measurement results of the three parties are used for estimating the phase error rate in the photon transmission process; the sum of the two error rates is defined as the total error rate in the degree of freedom; if the total error rate of the safety detection photons in any degree of freedom exceeds a set threshold value, the transmission process of the photons is proved to be unsafe, communication is stopped, and the original secret key is discarded by a user; if the total error rate of the two degrees of freedom is lower than a set threshold value, the photon transmission process is proved to be safe, and the next step is carried out;
and 6, carrying out error correction and private amplification on the public channel by the user 1, the user 2 and the user 3 to form a final security key.
2. The quantum secret sharing method based on the super-entanglement assist as claimed in claim 1, wherein: the user 1 uses the super-entanglement source to prepare the polarization-momentum super-entangled GHZ state
Figure FDA0003495034590000021
Wherein, | ψ1 +>PBelonging to one of 8 polarized GHZ states, and the expressions of the 8 polarized GHZ states under the Z group and the X group are respectively as follows:
Figure FDA0003495034590000022
Figure FDA0003495034590000023
Figure FDA0003495034590000024
Figure FDA0003495034590000031
Figure FDA0003495034590000032
Figure FDA0003495034590000033
Figure FDA0003495034590000034
Figure FDA0003495034590000035
|H>、|V>is the basis vector of Z group, respectively represents the horizontal polarization and the vertical polarization of photons, | +/->P is the basis vector of the X group,
Figure FDA0003495034590000036
subscripts 1,2,3 represent the serial number of the photon;
|ψ1 +>M8 GHZ states belonging to momentum freedom, the form of the 8 momentum GHZ states under Z group and X group is:
Figure FDA0003495034590000041
Figure FDA0003495034590000042
Figure FDA0003495034590000043
Figure FDA0003495034590000044
Figure FDA0003495034590000045
Figure FDA0003495034590000046
Figure FDA0003495034590000047
Figure FDA0003495034590000051
wherein, | L>,|R>Is the basis vector of the Z group and respectively represents the left and right of momentum, | +/->MIs a basis vector of a diagonal basis, satisfies
Figure FDA0003495034590000052
Subscripts 1,2,3 represent the sequence number of the photon, respectively.
3. The quantum secret sharing method based on the super-entanglement assist as claimed in claim 1, wherein: in step 3, for the three-party shared non-safety detection of the super-entangled GHZ photon pair, the user 2 and the user 3 do no operation on the photons in the momentum degree of freedom, but perform the encoding operation in the polarization degree of freedom, and the four encoding operations in the polarization degree of freedom include:
Figure FDA0003495034590000053
Figure FDA0003495034590000054
Figure FDA0003495034590000055
Figure FDA0003495034590000056
after the coding is completed, the polarization GHZ state shared by the three-party users evolves to | psii ±>P(i ═ 1,2,3, 4); three-party users agree on | psi in advance1 +>P、|ψ1 ->P、|ψ2 +>P、|ψ2 ->P、|ψ3 +>P、|ψ3 ->P、|ψ4 +>P、|ψ4 ->PRepresenting 8 codes of 000, 001, 010, 011, 100, 101, 110, 111, respectively.
4. The quantum secret sharing method based on the super-entanglement assist as claimed in claim 1, wherein: in the step 4, the user 1, the user 2 and the user 3 realize complete GHZ state analysis of the polarization degree of freedom through momentum entanglement assistance, namely, 8 polarization GHZ states can be completely distinguished; three user places respectively have 4 single photon detectors, are user 1 respectively:
Figure FDA0003495034590000061
and (4) a user 2:
Figure FDA0003495034590000062
user 3:
Figure FDA0003495034590000063
each GHZ state corresponds to 8 different detector response conditions with equal probability; users 2 and 3 publish the single photon detector response conditions at the positions, and the user 1 combines the detector response conditions to estimate the encoded GHZ state
Figure FDA0003495034590000064
Thereby inferring the original key that user 2 and user 3 jointly delivered.
5. The quantum secret sharing method based on the super-entanglement assist as claimed in claim 1, wherein: in step 5, the security detection comprises:
user 1 publishes the location and measurement basis of the security detection photon pairs, and then the three users randomly select either the Z-basis or X-basis to measure the security detection photons in the pairs and publish the measurement results. In the degree of freedom of polarization and momentum, if the measurement base is a rectangular base, the three-party measurement result is used for estimating the bit error rate Q of the photon transmission processPb(QMb)，QPb(QMb) A probability that the three-way measurements are not all the same; if the measurement basis is a diagonal basis, the three-party measurement result is used for estimating the phase error rate Q of the photon transmission processPp(QMp)，QPp(QMp) Is equal to threeThe measurement result of square has even number | +>P(M)The probability of (d); the sum of the two error rates is defined as the total error rate Q in this degree of freedomPt＝QPb+QPp(QMt＝QMb+QMp) (ii) a If QPtOr QMtIf the value is higher than the set threshold value, indicating that the photon transmission process is unsafe, discarding the generated original secret key, and rechecking the channel; total error rate Q when two degrees of freedomPtAnd QMtAnd when the values are all lower than the set threshold value, the communication safety is indicated.
6. The quantum secret sharing method based on the super-entanglement assist as claimed in claim 1, wherein: in the method, the initial quantum state of the super-entangled photons and the coded detector response conditions of the users 2 and 3 are public information, the detector response condition of the user 1 is not public, and the polarization GHZ state shared by the users 2 and 3 after the coding is finished is only known by the user 1.
7. The quantum secret sharing method based on the super-entanglement assist as claimed in claim 1, wherein: secure key generation rate R of the methodsecThe expression is as follows:
Rsec＝Rsift[1-(1+f)H(Qt)]
wherein Q istRepresenting the total error rate, R, of the keysiftRepresenting the generation rate of the screening key, f is the error correction efficiency of the post-processing, f is 1.16, and h (x) is binary shannon entropy:
H(x)＝-x log2(x)-(1-x)log2(1-x).
the total error rate of the key is Qt＝(1-QPt)(1-QMt)。
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