Quantum key generation method based on entanglement compression based on generalized isometric tensor

Abstract

The present invention relates to the field of quantum key distribution (QKD) technology, and specifically discloses a quantum key generation method based on entanglement compression using a generalized isometric tensor, which compresses any entangled state into a single photon state or a Bell state. Specifically, the generalized isometric tensor w(w N1 ,w N2 )、w′(w′ N1 ,w′ N2 ) compresses #imgabs0# into #imgabs1# and single-photon states |0>, |1>. Meanwhile, #imgabs2# and single-photon states |0>, |1> can be completely decompressed into #imgabs4# by #imgabs3#. Not only are the compression and decompression processes very simple, but entanglement compression using generalized isometric tensors can be implemented using quantum circuits and current technology. Our protocol can encode more classical bits than single photons used in general protocols, significantly improving coding efficiency and reducing the use of quantum resources. Our proposed QKD protocol also maintains the perfect security of the generated keys.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum key distribution (QKD), and in particular to a quantum key generation method based on entanglement compression of generalized isometric tensors. Background Art

[0002] Some scholars have proposed a method to generate an entangled state of a set of more than two particles, namely the Greenberger-Horne-Zeilinger (GHZ) state. A central question in the study of QKD based on entangled states is whether the entangled state can be compressed into a single-photon state. Some scholars have shown that entanglement compression can be achieved by constructing a mapping between the isometries of the multiscale entanglement renormalization hypothesis (MERA) and the local tensors of the matrix product operator (MPO). Although quantum data compression brings many advantages, it also brings challenges. The most important is its security. Some scholars have proposed a class of number-state trace-preserving tensor networks that can be used as classifiers in supervised learning, but he found that the product state of the entangled state cannot link the intermediate state to the classical data, which means a loss of interpretability. However, it is this loss of interpretability that can be used to ensure the security of QKD. Summary of the invention

[0003] The present invention provides a quantum key generation method based on entanglement compression of generalized isometric tensors, and the technical problem solved is: how to ensure the security of QKD without losing interpretability.

[0004] In order to solve the above technical problems, the present invention provides a quantum key generation method based on generalized isometric tensor for entanglement compression, comprising the steps of:

[0005] S1. Alice uses the first generalized isometry tensor to compress the N-photon GHZ entangled state into single-photon states |0> and |1> or uses the second generalized isometry tensor to compress the N-photon GHZ entangled state into Bell states, N ≥ 3;

[0006] S2. Alice sends the compressed single-photon state to Bob through a quantum channel, where Alice and Bob agree on the relationship between the compressed single-photon states |0> and |1> and the decompressed information; or, Alice sends one photon in each compressed Bell state to Bob through a quantum channel, and keeps the other one for herself, where Alice and Bob agree on the relationship between the compressed Bell state and the decompressed information; these compressed states transmitted through the quantum channel, i.e., compressed single-photon states or Bell states, are protected by decoy states;

[0007] S3. After receiving a compressed state, Bob randomly selects a basis to measure it, and then uses the authentication broadcast channel to tell Alice the basis he selected, and further performs basis matching. After basis matching, Alice notifies Bob through the authentication broadcast channel of the isometric tensor used to decompress the corresponding compressed state. Finally, Alice and Bob use the inverse mapping of the first generalized isometric tensor or the inverse mapping of the second generalized isometric tensor to decompress the compressed state finally selected;

[0008] S4. Alice and Bob obtain the bit information corresponding to the decompressed state according to the agreement in step S2, and concatenate them together to obtain the key.

[0009] Preferably, the first generalized isometric tensor is expressed as w(w N1 ,w N2 ),in:

[0010]

[0011]

[0012] w(w N1 ,w N2 ) satisfies the inner product trace-preserving mapping and also satisfies the following conditions:

[0013]

[0014] Among them, ν in , ν out They represent the input quantum state and the output quantum state respectively, w is w(w N1 ,w N2 ), is the inverse mapping of w, w:ν in → out It indicates that the first generalized isometric tensor is used to compress any input quantum state, i.e., an N-photon GHZ entangled state, into an output quantum state, i.e., a single-photon state, and I is a second-order identity matrix;

[0015] and,

[0016]

[0017] The inverse mapping of the first generalized isometric tensor is used to decompress any output quantum state, i.e., a single-photon state, into an input quantum state, i.e., an N-photon GHZ entangled state.

[0018] Preferably, the second generalized isometric tensor is expressed as w′(w′ N1 ,w′ N2 ),in:

[0019]

[0020]

[0021] In the isometric tensor w′ N1 The number of non-zero elements in the second and third rows is 2 N-1 -1, in the isometric tensor w′ N2 The first and fourth rows have 2 non-zero elements. N-1 -1,

[0022] w′(w′ N1 ,w′ N2 ) satisfies the inner product trace-preserving mapping and also satisfies the following conditions:

[0023]

[0024] w′ is w′(w′ N1 ,w′ N2 ), w′:v in →v out It indicates that the second generalized isometric tensor is used to compress any input quantum state, i.e., N-photon GHZ entangled state, into an output quantum state, i.e., Bell state;

[0025] and,

[0026]

[0027] The inverse mapping of the second generalized isometric tensor is used to decompress any output quantum state, namely the Bell state, into an input quantum state, namely the N-photon GHZ entangled state.

[0028] Preferably, in step S2, the relationship between the compressed single photon states |0> and |1> and the decompression information;

[0029] When the selected squeezed states are single-photon states |0> and |1>, |0> and |1> are decompressed to obtain N bits of classical information 00…0 and 11…1 respectively.

[0030] Preferably, in step S2, the relationship between the compressed Bell state and the decompressed information is:

[0031] When the selected compressed state is When Decompression yields N bits of classical information 00…0 and 11…1.

[0032] Preferably, in step S2, the measures taken to protect the compressed single-photon state or Bell state from the trapped state are:

[0033] Alice randomly selects decoy states and randomly inserts them into the compressed single-photon state sequence or Bell state sequence, and records the position and initial state of these decoy states. Once Bob confirms receipt of the particle, Alice announces the position of the decoy state and the measurement basis for measuring these decoy states. After Bob completes the measurement, he notifies Alice of his measurement results through the authenticated broadcast channel. By comparing the initial state of the decoy state with the state measured by the participants, Alice calculates the error rate of these decoy states. If the error rate is higher than a certain threshold, the protocol is terminated, otherwise it continues.

[0034] Preferably, the decoy state is in two bases B z ={0>,|1>}, B x {+>,|->} is randomly generated, where

[0035] The quantum key generation method based on entanglement compression of generalized isometric tensors provided by the present invention has the following effects:

[0036] 1. Not only is the compression and decompression process very simple, but entanglement compression using generalized isometric tensors can be implemented using quantum circuits and current technology. Since many ideas for quantum information processing devices are based on sending quantum information between network nodes with a relatively small quantum processor, finding a protocol for compressing transmitted quantum data is of great practical significance;

[0037] 2. QKD, which compresses the entangled state into a single-photon state, can achieve anti-decoherence;

[0038] 3. Compress any entangled state into a single photon state or Bell state before sending it to the receiver. This operation greatly reduces the number of quantum photons that need to be transmitted and stored, and has lower quantum transmission and quantum storage overhead;

[0039] 4. The compressed state not only reduces the number of quantum bits that need to be transmitted and stored, but also adds an additional qualitative property - that is, it increases the encoding capacity of the QKD protocol, which simultaneously achieves the requirements of multi-mode storage and secure transmission.

[0040] In simple terms, our protocol can encode more classical bits than the single photons used in general protocols, thereby significantly improving the coding efficiency and reducing the use of quantum resources. Our proposed QKD protocol also maintains the perfect security of the generated keys. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a schematic diagram of an N-photon GHZ entangled state provided by an embodiment of the present invention being randomly compressed into a number state |0> or |1> and |0> or |1> being decompressed into an N-photon GHZ entangled state;

[0042] Figure 2 The N-photon GHZ entangled state provided by the embodiment of the present invention is randomly compressed into a Bell state or and or Schematic diagram of the N-photon GHZ entangled state being decompressed. DETAILED DESCRIPTION

[0043] The following specifically illustrates the implementation mode of the present invention in conjunction with the accompanying drawings. The embodiments are provided for illustrative purposes only and are not to be construed as limitations of the present invention. The accompanying drawings are provided for reference and illustration only and do not constitute limitations on the scope of patent protection of the present invention, because many changes may be made to the present invention without departing from the spirit and scope of the present invention.

[0044] The embodiment of the present invention provides a quantum key generation method based on generalized isometric tensor for entanglement compression, comprising the steps of:

[0045] S1. Alice uses the first generalized isometry tensor to compress the N-photon GHZ entangled state into single-photon states |0> and |1> or uses the second generalized isometry tensor to compress the N-photon GHZ entangled state into Bell states, N ≥ 3;

[0046] S2. Alice sends the compressed single-photon state to Bob through a quantum channel, where Alice and Bob agree on the relationship between the compressed single-photon states |0> and |1> and the decompressed information; or, Alice sends one photon in each compressed Bell state to Bob through a quantum channel, and keeps the other one for herself, where Alice and Bob agree on the relationship between the compressed Bell state and the decompressed information; these compressed states transmitted through the quantum channel, i.e., compressed single-photon states or Bell states, are protected by decoy states;

[0047] S3. After receiving a compressed state, Bob randomly selects a basis to measure it, and then uses the authentication broadcast channel to tell Alice the basis he selected, and further performs basis matching. After basis matching, Alice notifies Bob through the authentication broadcast channel of the isometric tensor used to decompress the corresponding compressed state. Finally, Alice and Bob use the inverse mapping of the first generalized isometric tensor or the inverse mapping of the second generalized isometric tensor to decompress the compressed state finally selected;

[0048] S4. Alice and Bob obtain the bit information corresponding to the decompressed state according to the agreement in step S2, and concatenate them together to obtain the key.

[0049] Among them, the part compressed into the single-photon state is called the first QKD protocol in this example, and the part compressed into the Bell state is called the second QKD protocol in this example.

[0050] Before introducing the two QKD protocols, this example first introduces what is an isometric matrix and the two generalized isometric tensors that will be used in this example.

[0051] Definition 1. (Isometry Matrix) Given a d1×d2 matrix ω, such that (when d1<d2) or (When d1>d2), then ω is called an isometric matrix, is the inverse mapping of ω, is the second-order identity matrix.

[0052] For example, let Available So ω is an isometry matrix. Here isometry refers to the inner product (modulus) trace-preserving mapping, that is

[0053]

[0054] Here, |ψ> and |Φ> represent two quantum states in the large space. The isometric matrix ω maps |ψ> and |Φ> to the states in the small space as ω|ψ> and ω|Φ>, and the inner product of |ψ> and |Φ> <Φ|ψ> is equal to the inner product of ω|ψ> and ω|Φ> That is, the isometry matrix ω ensures that the inner product of two quantum states in a small space is equal to the inner product of their images mapped to a large space.

[0055] The concept of isometric matrices can be extended to the following generalized isometric tensors.

[0056] Definition 2. (The first generalized isometric tensor is the first generalized isometric tensor) The first generalized isometric tensor w(w N1 ,w N2 ), N≥3 is defined as follows:

[0057]

[0058]

[0059] In the present invention, the first generalized isometric tensor w(w N1 ,w N2 ) is used to realize entanglement compression. Obviously, w(w N1 ,w N2 ) is not an invertible mapping, but it can derive an inverse mapping The inverse mapping can be used to N1 ,w N2 ) compressed state is decompressed.N1 ,w N2 ) meets the following conditions:

[0060]

[0061] where ν in , ν out represent the input quantum state and the output quantum state respectively.

[0062] and,

[0063]

[0064] The first generalized isometric tensor can be used to compress any N-photon GHZ entangled state into a single-photon state.

[0065] Definition 3. (The second generalized isometric tensor is the second generalized isometric tensor) The second generalized isometric tensor w′(w′ N1 ,w′ N2 ) is defined as follows:

[0066]

[0067] Note that in the isometric tensor w′ N1 The number of non-zero elements in the second and third rows is 2 N-1 -1.

[0068]

[0069] Note that in the isometric tensor w′ N2 The first and fourth rows have 2 non-zero elements. N-1 -1.

[0070] Note that w′(w′ N1 ,w′ N2 ) meets the following conditions:

[0071]

[0072]

[0073] The second generalized isometric tensor can be used to compress any N-photon GHZ entangled state into a Bell state.

[0074] The first QKD protocol described

[0075] Given N photon GHZ entangled states with N ≥ 3, the first QKD protocol is performed as follows.

[0076] Step 1: Prepare squeezed single-photon states.

[0077] This step is performed by Alice. Using the first isometric tensor w(w N1 ,w N2 ), the N photon GHZ entangled state is compressed by Alice into the number states |0> and |1> (see Figure 1 ).Right now Use w(w N1 ,w N2 ) is compressed into the number states |0> and |1>, and the specific mathematical expression is:

[0078]

[0079]

[0080] Step 2: Transmission of compressed single-photon states.

[0081] Alice sends the compressed single photon state to Bob through a quantum channel. Here, Alice and Bob agree:

[0082] When the compressed states are the number states |0> and |1>, they are decompressed to obtain N bits of classical information 00…0 and 11…1 respectively.

[0083] These transmissions of squeezed single photon states through the quantum channel are protected by the trapped states. See step 3 below for details.

[0084] Step 3: Decoy state for eavesdropping detection.

[0085] Alice in B z ={|0>,|1>}, B x {|+>,|->} randomly selects a basis as a decoy state, where The decoy states are then randomly inserted into the compressed single-photon state sequence, and the positions and initial states of these decoy states are recorded. Once Bob confirms receipt of the particle, Alice announces the positions of the decoy states and the measurement basis for measuring these decoy states. After Bob completes the measurement, he notifies Alice of his measurement results through the authenticated broadcast channel. By comparing the initial state of the decoy state with the state measured by the participants, Alice can calculate the error rate of these decoy states. If the error rate is higher than a certain threshold, the protocol is terminated, otherwise it continues.

[0086] Step 4: Measurement of the squeezed entangled state.

[0087] This step is similar to the corresponding step in BB84. After receiving a compressed entangled state, Bob randomly selects a basis to measure it. Next, Bob tells Alice his selected basis using the authenticated broadcast channel. Finally, after the basis is matched, Alice informs Bob through the authenticated broadcast channel of the isometric tensor used to decompress the corresponding compressed entangled state. Finally, they use The compressed entangled state finally selected after decompression is as follows:

[0088]

[0089]

[0090] An example of the whole process is shown in Table 1.

[0091] Table 1 Example of compressed entangled states used to generate a key between Alice and Bob

[0092]

[0093] Step 5: Key negotiation.

[0094] In this step, consider the classical bit information encoded in the N-photon-GHZ state. When Alice and Bob decompress the selected single photons, they get When they use the agreement in step 2, they can get the classic information 00…0 and 11…1, and concatenate them together to get the key.

[0095] Second QKD protocol description

[0096] This example describes an alternative protocol for compressing any N-photon GHZ state into Bell states (see Figure 2 ). In fact, much of quantum information theory is related to quantum data operations under local constraints, so our protocol is naturally related to these studies. For any entangled state, we show a way to optimally compress them based on the second generalized isometric tensor we define, and make full use of the correlation between the compressed Bell states between Alice and Bob to achieve QKD. The steps of our second QKD protocol are as follows.

[0097] Step 1: Prepare squeezed Bell states.

[0098] First, the squeezed Bell states of odd and even bits are This step is performed by Alice. Using the second generalized isometric tensor w′(w′) shown in equations (6) and (7), N1 ,w′ N2 ), the N photon GHZ state is compressed into a Bell state by Alice (see Figure 2). This is because any N-photon GHZ state can be transformed into a matrix w′(w′ N1 ,w′ N2 ) is a 4×2 Ν , so the rows and columns of w′V are 4×1, and can be further converted into Bell states.

[0099] In the 3-photon GHZ state, For example, its matrix expression is

[0100] Alice uses w′(w3′1,w3′2) to convert the 3-photon GHZ state Compress to The specific mathematical expression is:

[0101]

[0102]

[0103] Step 2: Transmission of compressed Bell states.

[0104] Alice sends one photon in each compressed Bell state to Bob through the quantum channel, and keeps the other one for herself. Here, Alice and Bob agree:

[0105] When the compressed Bell states are obtained, Decompressed respectively, we get N bits of classical information 00…0 and 11…1.

[0106] These squeezed Bell state entangled photons transmitted through the quantum channel are protected by the trapped state, as detailed in step 3 below.

[0107] Step 3: Decoy state for eavesdropping detection.

[0108] Alice in B z ={|0>,|1>}, B x {|+>,|->} randomly selects a basis as a decoy state, where The decoy states are then randomly inserted into the compressed Bell state sequence, and the positions and initial states of these decoy states are recorded. Once Bob confirms receipt of the particle, Alice announces the positions of the decoy states and the measurement basis for measuring these decoy states. After Bob completes the measurement, he notifies Alice of his measurement results through the authenticated broadcast channel. By comparing the initial states of the decoy states with the states measured by the participants, Alice can calculate the error rate of these decoy states. If the error rate is higher than a certain threshold, the protocol is terminated, otherwise it continues.

[0109] Step 4: Measurement of the compressed Bell states.

[0110] This step is similar to the corresponding step in BBM92. After receiving a compressed entangled state photon, Bob randomly selects a basis to measure it. Next, Bob tells Alice the basis he chose using the authenticated broadcast channel. Then, after matching the basis, according to the agreement in step 2, Alice and Bob can obtain the corresponding compressed Bell state. Finally, Alice informs Bob through the authenticated broadcast channel that the isometric tensor is used to decompress the corresponding compressed entangled state, that is, they use Decompress the compressed Bell state that is finally selected. Here, we take equations (12) and (13) as examples to obtain the following equation:

[0111]

[0112] Note that in the isometric tensor w′ N1 The number of non-zero elements in the second and third rows is 2 N-1 -1.

[0113]

[0114]

[0115]

[0116] Step 5: Key negotiation.

[0117] In this step, we consider the classical bit information encoded in the N-photon GHZ state. When Alice and Bob decompress the selected single photon into According to the agreement in step 2, they can obtain the classic information 00…0 and 11…1, and concatenate them together to get the generated key.

[0118] Safe against measurement attacks:

[0119] The measurement attack is defined as Eve measuring the transmitted photons to obtain the squeezed states |0> and |1> or Bell states. According to the description of step 3 in our two protocols, the transmitted squeezed states or entangled photons are protected by the decoy states. In this sequence, the decoy states are obtained by Alice by converting the two basis B z ={0>,|1>}, B x {+>,|->} are randomly generated. Since the decoy state is an entangled photon randomly inserted into the squeezed number state or Bell state, Eve does not know the position and basis of each photon. Therefore, Eve has The probability of using the wrong basis to measure the decoy state, resulting in a change in the decoy state. Assume that the probability of choosing an incorrect basis is At the same time, the probability that Eve gets the correct state is (That is, the error probability is ), so for any decoy state, the probability of getting its correct state is That is, the error rate is According to current technology, the noise rate of actual quantum channels is about 2% to 8.9%, which is much lower than 75%, so Alice and Bob can easily detect measurement attacks.

[0120] Safely resist interception and retransmission attacks:

[0121] In this attack, in order to pass the eavesdropping inspection, Eve intercepts the decoy state photons sent on the quantum channel and retransmits the decoy states she prepared. Eve first observes the decoy state sequence sent by Alice, selects one from them, replaces the selected decoy states with the decoy states she prepared, and sends her own prepared states to Bob. However, since Eve does not know the position and basis of each decoy state, according to the no-cloning principle, she cannot forge the same decoy state. When Bob measures these decoy states forged by Eve, the error rate is According to current technology, the noise rate of actual quantum channels is about 2% to 8.9%, which is much lower than 75%, so Alice and Bob can easily detect the interception and retransmission attack.

[0122] Safe against entanglement and measurement attacks:

[0123] In this attack, suppose that in our proposed second protocol Eve exploits the entanglement of an auxiliary state |A> E ,|B> E ,|C> E ,|D> E Creating a new entangled state This new entangled state can be expressed as follows:

[0124] |ψ> ABC =|00> AB |A> E +|11> AB |B> E +|01> AB |C> E +|10> AB |D> E (18)

[0125] In odd positions, if Alice and Bob use base B z Correctly measured the Bell state The measurement results of the entangled photons between Alice and Bob should be exactly the same, and equation (18) becomes:

[0126] |ψ> ABE =|00> AB |C> E +|11> AB |D> E (19)

[0127] If Alice and Bob use base B x Correctly measured the Bell state For the entangled photons in , we have:

[0128]

[0129] That is, the ideal Bell state obtained by Alice and Bob has nothing to do with the photons entangled by Eve.

[0130] In an even position, if Alice and Bob use base B z Correctly measured the Bell state The measurement results of the entangled photons between Alice and Bob should be exactly the same, and equation (18) becomes:

[0131] |ψ> ABE =|01> AB |C> E +|10> AB |D> E (twenty one)

[0132] If Alice and Bob use base B x Correctly measured the Bell state For the entangled photons in , we have:

[0133]

[0134] That is, the ideal Bell state obtained by Alice and Bob has nothing to do with the photons entangled by Eve.

[0135] Therefore, entanglement and measurement attacks are invalid in our protocol.

[0136] Compression and decompression analysis:

[0137] Our QKD protocol can compress any entangled state into a single-photon state or Bell state using isometric tensors. Specifically, we use the generalized isometric tensor w(w N1 ,w N2 )、w′(w′ N1 ,w′ N2 )Will Compress to and single photon states |0>, |1>. At the same time, and the single-photon states |0>, |1> can be obtained by Completely decompressed to

[0138] Not only are the compression and decompression processes very simple, but entanglement compression using generalized isometric tensors can be implemented using quantum circuits and current technology. Since many ideas for quantum information processing devices are based on sending quantum information between network nodes using a relatively small quantum processor, finding protocols for compressing transmitted quantum data is of great practical interest. More generally, much of quantum information theory involves operating on data under local constraints, so our protocol proposed here naturally relates to these research needs.

[0139] Anti-decoherence analysis:

[0140] In the Ekert91 and BBM92 protocols and the GHZ state-based QKD protocol, the entangled state is required to be resistant to decoherence. However, entangled particles interact during actual transmission and storage, which leads to decoherence (or entanglement degradation) between the particles of the entangled system. This can be avoided in our first protocol because the entangled state is compressed into a single photon state. Therefore, our protocol is resistant to decoherence.

[0141] Low quantum transmission and quantum storage overhead:

[0142] For the Ekert91, BBM92 protocols and the GHZ state-based QKD protocol, each photon can only generate two keys at most, so a large number of photons need to be transmitted and stored. Our protocol first compresses any entangled state into a single photon state or Bell state before sending it to the receiver. This operation greatly reduces the number of quantum photons that need to be transmitted and stored. Instead, we use the corresponding isometric tensor to achieve a significant reduction in the number of quantum photons that need to be transmitted and stored. It is well known that classical transmission and storage overheads are much lower than quantum overheads. Therefore, our QKD protocol has lower quantum transmission and quantum storage overheads.

[0143] High encoding capacity:

[0144] For the BB84, Ekert91 and BBM92 protocols, as well as the GHZ state-based QKD protocol, each photon can only encode 1 bit of classical information, which greatly limits the practical efficiency of the QKD protocol. In contrast, in our protocol, a compressed number state |0> or |1> or Can be encoded into multiple bits of classical information. The compressed state not only reduces the number of qubits that need to be transmitted and stored, but also adds an additional qualitative property - that is, it increases the encoding capacity of the QKD protocol. This simultaneously achieves the requirements of multi-mode storage and secure transmission.

[0145] In summary, in this paper, we studied the problem of performing compression on entangled state sources in QKD protocols. We found that the compression correlation in QKD protocols can be used to improve the encoding power of the well-known BB84 and BBM92. The advantage of our protocol is that any entangled state can be compressed into and single photon states |0>, |1>. This approach is more efficient in terms of the number of quantum states used than traditional QKD using entangled states. At the same time, we show how to obtain a similar isometric tensor to obtain the decompressed compressed entangled state. In addition, combined with the isometric tensor, we can also obtain the coefficients of the entangled state, overcoming other major limitations of entanglement compression. Most importantly, the tensor network constructed by the isometric tensor is equivalent to a quantum circuit, making our proposed protocol feasible under current technology. Our proposed protocol also simultaneously achieves the requirements of multi-mode storage and deterministic transmission.

[0146] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A quantum key generation method based on entanglement compression using generalized isometric tensors, characterized in that: Includes steps: S1. Alice uses the first generalized isometry tensor to compress the N-photon GHZ entangled state into single-photon states |0 and |1> or uses the second generalized isometry tensor to compress the N-photon GHZ entangled state into Bell state, N≥3; the first generalized isometry tensor is expressed as w(w N1 ,w N2 ),in: w(w N1 ,w N2 ) satisfies the inner product trace-preserving mapping and also satisfies the following conditions: Among them, ν in , ν out They represent the input quantum state and the output quantum state respectively, w is w(w N1 ,w N2 ), is the inverse mapping of w, w:ν in → out It indicates that the first generalized isometric tensor is used to compress any input quantum state, i.e., an N-photon GHZ entangled state, into an output quantum state, i.e., a single-photon state, and I is a second-order identity matrix; and, The inverse mapping of the first generalized isometric tensor is used to decompress any output quantum state, i.e., a single photon state, into an input quantum state, i.e., an N-photon GHZ entangled state; The second generalized isometric tensor is denoted as w′(w′ N1 ,w′ N2 ),in: In the isometric tensor w′ N1 The number of non-zero elements in the second and third rows is 2 N-1 -1, in the isometric tensor w′ N2 The first and fourth rows have 2 non-zero elements. N-1 -1, w′(w′ N1 ,w′ N2 ) satisfies the inner product trace-preserving mapping and also satisfies the following conditions: w′ is w′(w′ N1 ,w′ N2 ), w′:v in →v out It indicates that the second generalized isometric tensor is used to compress any input quantum state, i.e., N-photon GHZ entangled state, into an output quantum state, i.e., Bell state; and, The inverse mapping of the second generalized isometric tensor is used to decompress any output quantum state, i.e., Bell state, into an input quantum state, i.e., an N-photon GHZ entangled state; S2. Alice sends the compressed single-photon state to Bob through a quantum channel, where Alice and Bob agree on the relationship between the compressed single-photon states |0> and |1> and the decompressed information; or, Alice sends one photon in each compressed Bell state to Bob through a quantum channel, and keeps the other one for herself, where Alice and Bob agree on the relationship between the compressed Bell state and the decompressed information; these compressed states transmitted through the quantum channel, i.e., compressed single-photon states or Bell states, are protected by decoy states; S3. After receiving a compressed state, Bob randomly selects a basis to measure it, and then uses the authentication broadcast channel to tell Alice the basis he selected, and further performs basis matching. After basis matching, Alice notifies Bob through the authentication broadcast channel of the isometric tensor used to decompress the corresponding compressed state. Finally, Alice and Bob use the inverse mapping of the first generalized isometric tensor or the inverse mapping of the second generalized isometric tensor to decompress the compressed state finally selected; S4. Alice and Bob obtain the bit information corresponding to the decompressed state according to the agreement in step S2, and concatenate them together to obtain the key.

2. The method for generating quantum keys based on entanglement compression using generalized isometric tensors according to claim 1, characterized in that: In step S2, the relationship between the compressed single-photon states |0〉 and |1〉 and the decompressed information; When the selected squeezed states are single-photon states |0> and |1>, |0> and |1> are decompressed to obtain N bits of classical information 00…0 and 11…1 respectively.

3. The method for generating quantum keys based on entanglement compression using generalized isometric tensors according to claim 2, characterized in that: In step S2, the relationship between the compressed Bell state and the decompressed information is: When the selected compressed state is When Decompression yields N bits of classical information 00…0 and 11…1.

4. The method for generating quantum keys based on entanglement compression using generalized isometric tensors according to claim 2, characterized in that: In step S2, the measures taken to protect the compressed single-photon state or Bell state from the trapped state are: Alice randomly selects decoy states and randomly inserts them into the compressed single-photon state sequence or Bell state sequence, and records the position and initial state of these decoy states. Once Bob confirms receipt of the particle, Alice announces the position of the decoy state and the measurement basis for measuring these decoy states. After Bob completes the measurement, he notifies Alice of his measurement results through the authenticated broadcast channel. By comparing the initial state of the decoy state with the state measured by the participants, Alice calculates the error rate of these decoy states. If the error rate is higher than a certain threshold, the protocol is terminated, otherwise it continues.

5. The method for generating quantum keys based on entanglement compression using generalized isometric tensors according to claim 4, characterized in that: The decoy state is in two bases B z ={0>,|1>}, B x {+>,|->} is randomly generated, where

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