Method for bidirectionally, controllably, symmetrically and invisibly transmitting two three-quantum-bit target quantum states based on nine-quantum-bit entangled channel

Abstract

The invention relates to the technical field of quantum communication, and discloses a method for bidirectionally, controllably, symmetrically and invisibly transmitting two three-quantum-bit target quantum states based on a nine-quantum-bit entangled channel. According to the method, a quantum channel is constructed by using nine-quantum-bit entanglement resources, so that controllable symmetric invisible transmission of two unknown three-quantum-bit exclusive target states is realized, and quantum measurement used in the implementation process only comprises single-quantum-bit measurement and Bell state measurement. The used quantum operation only comprises single quantum bit bubble operation and two quantum bit gate operation, the measurement and operation are realized in a quantum experiment, and the bidirectional controllable quantum teleportation method provided by the invention is large in information capacity, high in transmission efficiency, low in execution difficulty and high in feasibility and practicability.

Description

Technical Field

[0001] The present invention relates to the field of quantum communication technology, and more specifically, to a method for bidirectionally controllable symmetrical stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel. Background Art

[0002] Quantum entanglement is a special phenomenon in the quantum world, and no classical thing can correspond to it. As an important quantum resource, it is widely used in various branches of quantum communication, such as quantum key distribution, quantum secure direct communication, remote state preparation, quantum cloning, quantum identity authentication, quantum operation transmission and sharing, etc. In particular, in 1993, Bennett and other research groups proposed a new concept of quantum communication, called quantum teleportation (QST). In the QST task, the quantum state of unknown information can be transmitted remotely only by relying on the previously shared quantum entanglement resources and classical communication and some necessary local quantum operations. Using QST technology, not only can the secure transmission of quantum information and classical information be achieved, but also quantum resources can be remotely distributed in quantum networks. Therefore, in the past two decades, QST has gained a large number of followers and has been widely studied in experiments and theories.

[0003] Different from the general QST, Zha et al. proposed a special QST scheme in 2013 using a five-qubit cluster state as a quantum channel. In this scheme, under the control of a supervisor, two legal communication users can simultaneously transmit their unknown quantum states to each other. This scheme is called the bidirectional controllable quantum teleportation (BCQST) scheme. Compared with the previous QST scheme, BCQST has two major advantages. First, BCQST has an additional communication controller, which is equivalent to a third-party trading platform in business or a command center in the military. It has the function of supervising and controlling the two communicating parties, which to a certain extent enhances the security of traditional quantum teleportation. Second, BCQST can realize the bidirectional transmission of the target quantum state, that is, the first and second communication parties are both the sender and receiver of one quantum target state, and the receiver and sender of another quantum target state. This not only greatly improves the communication capacity, but also can be used for instant communication and interaction between the two communicating parties. That is to say, BCQST greatly broadens the efficiency and application scenarios of quantum teleportation. Based on the above two outstanding advantages, BCQST has developed rapidly in recent years, and domestic and foreign scholars have made a lot of research progress in this field.

[0004] According to the number of bits of the target quantum state to be transmitted, the existing BCQST schemes can be divided into the following types: (transmit 1 qubit target state to each other respectively); (transmitting 1 and 2 qubit target states to each other respectively); (Transmit 2 qubit target states to each other); (respectively transferring 2 and 3 qubit target states to each other). However, In other words, a common shortcoming of the existing BCQST scheme is that the number of target quantum states that can be transmitted simultaneously is relatively small, which leads to technical bottlenecks in the capacity and efficiency of BCQST. The applicable quantum scenarios are also limited to some extent, and cannot meet the needs of big data in future quantum networks.

[0005] It is particularly worth mentioning that, using a nine-qubit entangled state and two auxiliary single-qubit states as quantum resources, Zhang et al. proposed a large information capacity BCQST scheme in 2023 [from the paper Zhang, XH, Jin, WT, Zeng, HX, et al.: Cost-effective bidirectional controlled quantum teleportation scheme by using nine-qubit entangled state. International Journal of Theoretical Physics 62(5):95(2023)]. For the convenience of description, we call it the ZJZFY-BCQST scheme. Compared with the existing BCQST scheme, the ZJZFY-BCQST scheme has the characteristics of more bits of target quantum states that can be transmitted, higher efficiency, and larger communication capacity. However, the ZJZFY-BCQST scheme uses a five-qubit entangled state basis measurement. As we all know, it is still difficult to achieve experimental multi-qubit entangled state basis measurements greater than three in various quantum systems. Therefore, the experimental feasibility of the ZJZFY-BCQST scheme is not strong. In fact, the quantum measurement or quantum operation used to complete the bidirectional controllable quantum teleportation task is too complicated, resulting in low experimental feasibility of the scheme, which is another common defect of the existing BCQST scheme.

[0006] In summary, it is necessary for us to improve the existing BCQST scheme, increase communication capacity and transmission efficiency while reducing the complexity of necessary quantum measurements or quantum operations, so as to accelerate the practical application of bidirectional controllable quantum teleportation technology. Summary of the invention

[0007] The present invention provides a method for bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel, with the aim of solving some key technical problems in the practical application of bidirectional controllable quantum teleportation, including improving the capacity and transmission efficiency of quantum information to be transmitted, reducing the intensity and difficulty of necessary quantum measurements or quantum operations, and other performance technical indicators.

[0008] The present invention provides a method for bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel, comprising the following steps:

[0009] (1) Construct a nine-qubit entangled state as a quantum channel and rationally allocate quantum channel entanglement resources among the three communicating parties;

[0010] (2) The first communication party and the second communication party perform single-qubit orthogonal basis measurement and Bell state measurement on their qubits and inform each other of the measurement results through a classical channel;

[0011] (3) controlling the communication party to perform single-qubit computing-based measurement and publish its measurement results to the first communication party and the second communication party;

[0012] (4) the first communication party and the second communication party perform corresponding conversion operations;

[0013] (5) The first communication party and the second communication party perform a recovery operation to reconstruct the other party's three-qubit exclusive target state.

[0014] Furthermore, the preparation of the nine-qubit entangled state comprises the following steps:

[0015] Step S1-1, nine single quantum bits with an initial state of |0> are combined into a nine-qubit direct product state;

[0016] Step S1-2, perform Hadamard gate operation on quantum bit 1 Here {|0>,|1>} are two mutually orthogonal basis vectors of the single-qubit computation basis, and Then they are two mutually orthogonal basis vectors of the single-qubit orthogonal basis;

[0017] Step S1-3, four two-qubit controlled Harmon operations U are performed on qubits 1, 2, 4, 6, and 8, where qubit 1 is used as a control qubit and qubits 2, 4, 6, and 8 are used as target qubits. In the present invention, the two-qubit controlled Harmon operation U operator is defined as: in Quantum bit e is the control qubit, and qubit f is the target qubit;

[0018] Step S1-4, perform four two-qubit controlled NOT gate operations N on qubits 1, 3, 5, 7, and 9, where qubit 1 is used as the control qubit and qubits 3, 5, 7, and 9 are used as target qubits. In the present invention, the two-qubit controlled NOT gate operation N operator is defined as:

[0019] Among them, quantum bit g is the control quantum bit, and quantum bit h is the target quantum bit.

[0020] Step S1-5, perform four two-qubit controlled NOT gate operations N on the qubit pairs (2, 3), (4, 5), (6, 7), and (8, 9), respectively.

[0021] Furthermore, the three-qubit exclusive target states of the first communication party and the second communication party are respectively: and

[0022] Among them, α i and β i are plural and satisfy and Quantum bit a 1 、a 2 and a 3 Belongs to the first communication party, b 1 、b 2 and b 3 Belongs to the second communication party.

[0023] Furthermore, the quantum channel linking the first communication party, the second communication party and the control communication party is a nine-qubit entangled state prepared by the method described in step (1), which is expressed as follows:

[0024]

[0025] Among them, quantum bits 2, 4, 6, and 8 belong to the first communication party, 3, 5, 7, and 9 belong to the second communication party, and quantum bit 1 belongs to the control communication party. In the present invention,

[0026]

[0027] represents four mutually orthogonal Bell states, These constitute the four basis vectors of Bell state measurement;

[0028] Furthermore, the first communication party and the second communication party follow the following protocol in step (2): if the single-qubit orthogonal basis measurement result of one communication party is |+>, then a classical bit "0" is sent to the other communication party, otherwise a classical bit "1" is sent; if the Bell state measurement result of one communication party is Then the classic bits "00", "01", "10", "11" are sent to the other communication party.

[0029] Furthermore, in step (3), the control communication party follows the following protocol: if the single quantum bit computation basis measurement result is |0>, then he sends a classical bit "0" to the first communication party and the second communication party, otherwise he sends a classical bit "1".

[0030] Further, the first communication party and the second communication party respectively perform corresponding transformation operations on the quantum bits (3,5) and (6,8) according to the measurement results of the control communication party and the other party. r,s,t,x,y,q , which are all composed of four single-qubit operations {I,σ x ,σ y ,σ z}, in the present invention, I = |0><0| + |1><1| represents a unit operation, σ x =|0><1|+|1><0|,σ y =|0><1|-|1><0|,σ z =|0><0|-|1><1| represents three Pauli operations;

[0031] Furthermore, the first communication party and the second communication party respectively convert the quantum bit a 1 and b 2 The quantum state is fixed to and The specific process is: if the measurement result of the first communication party in step (2) is Then for quantum bit a 1 Perform a Hadamard gate operation H, otherwise perform a Pauli-Hadamard gate composite operation σ x H; If the measurement result of the second communication party in step (2) is Then for quantum bit b 2 Perform a Hadamard gate operation H, otherwise perform a Pauli-Hadamard gate composite operation σ x H.

[0032] Furthermore, the first communication party and the second communication party respectively perform their quantum bit pairs (6, a 1 ) and (3, b 2 ) Perform two two-qubit controlled NOT gate operations N, where qubits 6 and 3 are used as control qubits, and qubit a 1 and b 2 as a target quantum bit.

[0033] Furthermore, after the operation is completed, the quantum bit group (6, a 1 ,8) and (3,b2 , the quantum state of 5) is reconstructed as:

[0034]

[0035] That is, the target quantum state |ξ> of the first communication party has been successfully reconstructed in the quantum bit group (3, b 2 , 5), the target quantum state |χ> of the second communication party is also successfully reconstructed on the quantum bit group of the first communication party (6, a 1 , 8).

[0036] The present invention proposes a system for implementing quantum state information transmission processing, which is used to execute the above-mentioned method of bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel.

[0037] The beneficial effects of the present invention are as follows: the present method utilizes nine-qubit entangled resources to construct a quantum channel to realize the controllable symmetric invisible transmission of two unknown three-qubit exclusive target states. The quantum measurements used in the implementation process only include single-qubit measurements and Bell state measurements, and the quantum operations used only include single-qubit Pauli operations and two-qubit gate operations. These measurements and operations have long been realized in quantum experiments. The present invention has large information capacity, high transmission efficiency, low execution difficulty, and strong feasibility and practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a two-way controllable Technology roadmap for quantum teleportation methods;

[0039] Figure 2 It is a quantum circuit diagram corresponding to a method for preparing a nine-qubit entangled state;

[0040] Figure 3 is a Quantum flow chart of the method for bidirectional controllable quantum teleportation. DETAILED DESCRIPTION

[0041] The subject matter described herein will now be discussed with reference to example implementations. It should be understood that the discussion of these implementations is only to enable those skilled in the art to better understand and implement the subject matter described herein, and the functions and arrangements of the elements discussed may be changed without departing from the scope of protection of the present specification. Various examples may omit, replace, or add various processes or components as needed. In addition, the features described in some examples may also be combined in other examples.

[0042] The present invention proposes a The BCQST method requires breakthroughs in the following key technologies: First, it requires the use of multi-qubit entangled states as quantum channels, and the preparation of multi-qubit entangled resources is not simple; second, it is necessary to rationally arrange quantum resources. From a probabilistic point of view, the more quantum entangled bits there are, the greater their permutations and combinations, which leads to a more complex entangled structure of quantum resources. Among these entangled structures, some can be used to implement the BCQST scheme, while some cannot, and each entangled structure needs to be deeply analyzed; finally, even if the quantum entangled structure is available, complex local operations and quantum measurements are required for information extraction, transfer, and reconstruction.

[0043] The present invention discloses a method for bidirectional controllable quantum stealth transmission of two three-qubit exclusive target quantum states based on a nine-qubit entangled channel, including: constructing a nine-qubit entangled state as a quantum channel, and reasonably allocating quantum channel entanglement resources among the three communicating parties; the first communicating party and the second communicating party perform single-qubit orthogonal basis measurement and Bell state measurement on their qubits and inform each other of the measurement results through the classical channel; the controlling communicating party performs single-qubit computational basis measurement and publishes his measurement results to the first communicating party and the second communicating party; the first communicating party and the second communicating party perform corresponding conversion operations; the first communicating party and the second communicating party perform recovery operations to reconstruct the other party's three-qubit exclusive target state. This method uses nine-qubit entangled resources to construct a quantum channel to realize the controllable symmetric stealth transmission of two unknown three-qubit exclusive target states. The quantum measurements used in the implementation process only include single-qubit measurements and Bell state measurements, and the quantum operations used only include single-qubit Pauli operations and two-qubit gate operations. These measurements and operations have long been realized in quantum experiments. The present invention has low implementation difficulty and strong feasibility and practicality. The specific technical roadmap is as follows: Figure 1 As shown;

[0044] At least one embodiment of the present invention discloses a method for bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel, comprising:

[0045] (I) Preparation of nine-qubit entangled state

[0046] 1. Combine nine single qubits with an initial state of |0> into a nine-qubit direct product state

[0047]

[0048] 2. Perform Hadamard gate operation H= on qubit 1;

[0049] The Hadamard gate operation mentioned in the present invention is defined as in After performing the Hadamard gate H= operation on qubit 1, the initial nine-qubit direct state |Θ 0 > 123456789 Evolved into

[0050]

[0051] 3. Perform four two-qubit controlled Harman operations U on qubits 1, 2, 4, 6, and 8, where qubit 1 is used as the control qubit and qubits 2, 4, 6, and 8 are used as target qubits respectively;

[0052] In the present invention, the specific form of the two-qubit control Harman operation is:

[0053]

[0054] In this equation, e and f represent two qubits, where qubit e is the control qubit and qubit f is the target qubit. The specific form is

[0055]

[0056] After performing four two-qubit controlled Harman operations on qubits 1, 2, 4, 6, and 8, the quantum state |Θ 1 > 123456789 Evolved into

[0057]

[0058] 4. Perform four two-qubit controlled NOT gate operations N on qubits 1, 3, 5, 7, and 9, where qubit 1 is used as the control qubit and qubits 3, 5, 7, and 9 are used as target qubits respectively;

[0059] Here, the two-qubit controlled NOT gate operation N is defined as:

[0060]

[0061] In this equation, g and h represent two qubits, where qubit g is the control qubit and qubit h is the target qubit. I = |0><0|+|1><1| is a unit operation, and σ x =|0><1|+|1><0| is a Pauli operation. There are two more Pauli operations that will be used later. They are σ y =|0><1|-|1><0| and σ z =|0><0|-|1><1|.

[0062] After performing four two-qubit controlled NOT gate operations on qubits 1, 3, 5, 7, and 9, the quantum entangled state |Θ2 > 123456789 Further evolved into:

[0063]

[0064] 5. Perform four two-qubit controlled NOT gate operations N on the qubit pairs (2,3), (4,5), (6,7), and (8,9) respectively;

[0065] After these operations, the quantum entangled state |Θ 2 > 123456789 Finally, it evolves into the nine-qubit entangled channel state required for our second stage of three-party controllable bidirectional quantum teleportation.

[0066]

[0067] In the formula and are two Bell states. By the way, the other two Bell states are and They will be used in subsequent steps.

[0068] The specific quantum circuit diagram at this stage is as follows Figure 2 As shown;

[0069] (II) The second stage: based on the nine-qubit entangled channel Bidirectional controllable quantum teleportation method.

[0070] This method involves three legitimate users, whom we call Anne, Benson and Chris. Anne and Benson each have an exclusive 3-qubit target state that they want to transmit to each other, but considering information security issues, their communication must be supervised by an independent third party, Chris. That is to say, only with the consent and help of Chris can their idea of ​​transmitting their respective 3-qubit target states to each other be realized. It should be noted here that their respective exclusive 3-qubit target states are unknown to anyone, including themselves. Under the current qubit calculation basis, the forms of these two exclusive 3-qubit target quantum states can be expressed as:

[0071]

[0072] and

[0073]

[0074] In the above two equations, α i and β i are plural and satisfy and Quantum bit a 1 , a 2 and a 3 Belongs to Anne, quantum bit special b 1 , b 2 and b 3 The quantum channel connecting Anne, Benson and Chris is the 9-qubit entangled state prepared in the first stage.

[0075]

[0076] Among them, qubits 2, 4, 6 and 8 belong to Anne, qubits 3, 5, 7 and 9 belong to Benson, and qubit 1 belongs to Chris.

[0077] To achieve the above task, the three parties in communication, Anne, Benson, and Chris, can follow the steps below. The corresponding operation flow chart is as follows: Figure 3 shown.

[0078] Step 1: Anne first performs a 1 Make a single-qubit orthogonal basis {|+>,|->} measurement, and then measure her qubit pair (a 2 , 2) and (a 3 , 4) as a Bell state basis Measurement.

[0079] Before Anne's measurement, the quantum state of the entire system is:

[0080]

[0081] Through calculation, it can be concluded that after Anne's measurement, the quantum state of the remaining quantum bits collapses to:

[0082] Here, j,m,n,k,l∈{0,1},

[0083] and These are the two measurements with Anne and According to Anne's measurement results, the collapsed state There are 32 possible forms in total. For example, suppose Anne's measurement result is and Then the quantum state of the remaining qubits collapses to

[0084] here,

[0085]

[0086] Step 2: Anne sends her measurement results to Benson via the classical channel.

[0087] Anne and Benson reach an agreement in advance that if Anne's single-qubit orthogonal basis measurement result is |+>, then she sends a classical "0" to Benson. Otherwise, Anne sends a classical "1" to Benson. Similarly, if Anne's Bell state basis measurement result is or Then Anne sends the classic bits "00", "01", "10", "11". For example, if Anne's measurement result is and Then Anne sends the classic bit string information "11000" to Benson.

[0088] Step 3: Benson's quantum bit b 2 Make a single-qubit orthogonal basis measurement, and then measure her qubit pair (b 1 , 7) and (b 3 , 9) perform Bell state basis measurements.

[0089] Calculations show that after Benson's measurement, the quantum state of the remaining qubits collapses to:

[0090]

[0091] Here, r,s,t,x,y∈{0,1},

[0092] and These are the two measurements with Benson and For example, suppose Benson's measurement result is and Then the quantum state of the remaining quantum bits (6,8) collapses to

[0093]

[0094] One of the two.

[0095] Step 4: Benson sends his measurement results to Anne via the classical channel.

[0096] The specific transmission method is the same as step 2.

[0097] Step 5: Chris’s consent and assistance.

[0098] If Chris disagrees with Anne and Benson’s request, the task ends here. Otherwise, Chris performs a single-qubit computational basis {|0>,|1>} measurement on her qubit 1. It is easy to see from formula (9) that if Chris’s measurement result is | q >1( q =0,1), then the quantum states of the remaining quantum bits (3,5,6,8) collapse to Next, Chris announces her measurement results to Anne and Benson via classical channels.

[0099] Step 6: Anne and Benson perform corresponding transformation operations on their qubit pairs (3,5) and (6,8) respectively.

[0100] According to Chris and the other party's measurement results, Anne and Benson perform corresponding transformation operations on their quantum bits (3,5) and (6,8) to convert O j,m,n,k,l,q and O r,s,t,x,y,q , they are all composed of four single-qubit operations {I,σ x ,σ y ,σ z Table I lists the specific forms of the conversion operations corresponding to Anne and Benson in all possible cases.

[0101] Table I: Relationship between various possible measurement results and the collapsed states of the quantum bit pairs (3, 5) and (6, 8) in step 5 and the corresponding conversion operations.

[0102] Acting on quantum bit a 1 (b 2 ) on a single quantum bit orthogonal basis measurement result;

[0103] Acting on the quantum bit pair a 2 and 2(b 1 and 7) on the Bell state basis measurement results;

[0104] Acting on the quantum bit pair a 3 and 4(b 3 and 9) on the Bell state basis measurement results;

[0105] SCMR 1 : Single qubit computational basis measurement result acting on qubit 1;

[0106] CS: Step 5 collapsed state Specific expression of

[0107] TO: Convert.

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116] From Table I, we can easily calculate that in any case, the conversion operation can convert the collapsed state Transformed into

[0117]

[0118] here,

[0119] |P> 35 =(α 0 |00>+α 1 |01>+α 2 |10>+α 3 |11>) 35

[0120] |Q> 68 =(β 0 |00>+β 1 |01>+β 2 |10>+β 3 |11>) 68

[0121] Step 7: Actions taken by Anne and Benson to restore the target quantum state.

[0122] First, Anne and Benson each placed their quantum bit a 1 and b 2 The quantum state is fixed to and Specifically, if Anne (Benson)'s measurement result in the first step is Then she (he) has a 1 (b 2 ) performs a Hadamard gate operation On the contrary, if Anne (Benson)'s measurement result in the first step is Then she (he) has a 1 (b 2 ) performs a Pauli-Hadamard gate compound operation σ x H. So far, the quantum bit group (6, a 1 ,8) and (3,b 2 , 5) can be written as:

[0123]

[0124] Next, Anne and Benson tested their qubit pair (6, a 1 ) and (3, b 2 ) performs two two-qubit controlled NOT gate operations, where qubits 6 and 3 are used as control qubits, and qubit a 1 and b 2 As the target qubit. After the two controlled NOT gate operations of Anne and Benson, the qubit group (6, a 1 ,8) and (3,b 2 , the quantum state of 5) eventually evolves to

[0125]

[0126] From the above formula, it can be easily seen that Benson’s target state |χ> has perfectly reproduced Anne’s quantum bit group (6, a 1 , 8). At the same time, Anne's target quantum state |ξ> was also successfully reproduced in Benson's quantum bit group (3, b 2 , 5). So far, the task of bidirectional controllable quantum teleportation of two three-qubit exclusive entangled states has been perfectly achieved.

[0127] The following is an explanation of the benefits of the above technical solution of the present invention by comparing it with the technical solution in the prior art:

[0128] The key indicators for measuring the performance of a bidirectional controllable quantum teleportation scheme are: quantum resource consumption, classical resource consumption, target quantum state information capacity to be transmitted, operation complexity, and transmission efficiency. Under equivalent resource consumption, the larger the target quantum state information capacity, the higher the transmission efficiency, and the smaller the operation complexity, the better the performance of the bidirectional controllable quantum teleportation method. Conversely, under equivalent quantum and classical resource consumption, if the target quantum state information capacity is smaller, the transmission efficiency is lower, and the operation complexity is greater, the performance of the bidirectional controllable quantum teleportation method is worse.

[0129] The present invention proposes a method for bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel and a specific embodiment thereof: (1) the quantum resource is a self-made nine-qubit entangled state, that is, the quantum resource consumption parameter q R =9qubit. (2) The first communication party and the second communication party each need to perform two Bell state basis measurements and one single quantum bit basis measurement, while the control communication party only needs to perform one single quantum bit basis measurement. As we all know, single quantum bit basis measurement and Bell state basis measurement have long been implemented in various quantum physics experimental systems, such as particle trap systems, cavity QED systems, and optical systems. Therefore, the operation complexity of the present invention is low and the experimental feasibility is strong. (3) The publication of a single quantum bit basis measurement result and a Bell state basis measurement result corresponds to 1cbit and 2cbit of classical information, respectively. The present invention performs a total of three single quantum bit basis measurements and two Bell state basis measurements, corresponding to the classical resource consumption parameter c R =11 cbit. (4) The first communication party and the second communication party each symmetrically and stealthily transmit a three-qubit target quantum state to each other, that is, the information capacity parameter q to be transmitted T =6qubit. (5) The calculation formula for the transmission efficiency of bidirectional controllable quantum teleportation is: Substituting each parameter into the transmission efficiency of the bidirectional controllable quantum teleportation method proposed in the present invention is:

[0130] Under experimental conditions, we compared the above five performance indicators between the present invention and the large information capacity BCQST scheme [International Journal of Theoretical Physics 62(5):95(2023)] (abbreviated as ZJZFY-BCQST scheme) mentioned in the background art and the latest BCQST scheme [International Journal of Theoretical Physics 63(4):86(2024)] (abbreviated as JLZHFZYT-BCQST scheme). In the ZJZFY-BCQST scheme, a nine-qubit entangled state and two single-qubit auxiliary states were used as quantum resources, and two five-qubit entangled state basis measurements and one single-qubit basis measurement were performed, requiring the transmission of 11 bits of classical information, achieving bidirectional mutual transmission of a three-qubit target quantum state. In the JLZHFZYT-BCQST scheme, an eight-qubit entangled state is used as a quantum resource, two Bell state basis measurements and a three-qubit GHZ state measurement are performed, and eight bits of classical information need to be transmitted, achieving bidirectional mutual transmission of a two-qubit target quantum state. Table II lists the comparison of the bidirectional controllable quantum teleportation method of the present invention with the ZJZFY-BCQST scheme and the JLZHFZYT-BCQST scheme in terms of quantum resource consumption, classical resource consumption, transmittable quantum information capacity, necessary operation difficulty and transmission efficiency.

[0131] Table II: Performance parameter comparison of the solution of the present invention with large information capacity and the latest BCQST solution. QRC: Quantum

[0132] Resource consumption; SQM: single qubit basis measurement; BSM: Bell state basis measurement; TQGHZM: triple quantum ratio

[0133] Special GHZ state basis measurement; FQESM: Five-qubit entangled state basis measurement.

[0134]

[0135] As can be seen from Table II, the technical solution of the present invention has a large information capacity and high transmission efficiency. More importantly, the ZJZFY-BCQST scheme uses a five-qubit entangled state basis measurement (FQESM), and the JLZHFZYT-BCQST scheme uses a three-qubit GHZ state basis measurement (TQGHZM). These multi-qubit entangled state basis measurements are difficult to implement in terms of current experimental technology, that is, these two schemes are difficult to operate and have low experimental feasibility, while the technical solution of the present invention only needs to use single-qubit measurement and Bell state basis measurement that have been implemented in various experimental systems.

[0136] The above comparison of performance parameters with large information capacity and the latest BCQST scheme shows that the bidirectional controllable quantum teleportation method of the present invention has significant advantages such as large information capacity, high transmission efficiency, and strong experimental feasibility. Its various performances are excellent and are at the leading level at home and abroad.

[0137] The above describes an embodiment of the present invention, but this embodiment is not limited to the above-mentioned specific implementation mode. The above-mentioned specific implementation mode is merely illustrative and not restrictive. Under the guidance of this embodiment, ordinary technicians in this field can also make more forms of equivalent embodiments, all of which are within the protection of this embodiment.

Claims

1. A method for bidirectional controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel, characterized in that: include: (1) constructing a nine-qubit entangled state as a quantum channel and reasonably allocating quantum channel entanglement resources among the first communication party, the second communication party, and the control communication party; (2) The first communication party and the second communication party perform single-qubit orthogonal basis measurement and Bell state measurement on their qubits and inform each other of the measurement results through a classical channel; (3) controlling the communication party to perform single-qubit computational basis measurement and publishing the measurement result to the first communication party and the second communication party; (4) the first communication party and the second communication party perform corresponding conversion operations; (5) The first communication party and the second communication party perform a recovery operation to reconstruct the other party's three-qubit exclusive target state.

2. The method of bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel according to claim 1, characterized in that: The preparation of the nine-qubit entangled state in step (1) comprises the following steps: Step S1-1, nine single quantum bits with an initial state of |0> are combined into a nine-qubit direct product state; Step S1-2, performing a Hadamard gate operation H on quantum bit 1; Step S1-3, performing four two-qubit controlled Harmon operations U on qubits 1, 2, 4, 6, and 8, where qubit 1 is used as a control qubit, and qubits 2, 4, 6, and 8 are used as target qubits respectively; Step S1-4, performing four two-qubit controlled NOT gate operations N on qubits 1, 3, 5, 7, and 9, where qubit 1 is used as a control qubit and qubits 3, 5, 7, and 9 are used as target qubits respectively; Step S1-5, perform four two-qubit controlled NOT gate operations N on the qubit pairs (2, 3), (4, 5), (6, 7), and (8, 9), respectively.

3. The method of bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel according to claim 1, characterized in that: The three-qubit exclusive target states of the first communication party and the second communication party are respectively: and Among them, α i and β i are plural and satisfy and Quantum bits a1, a2 and a3 belong to the first communication party, and b1, b2 and b3 belong to the second communication party.

4. The method of bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel according to claim 1, characterized in that: The quantum channel linking the first communication party, the second communication party and the control communication party is the self-made nine-qubit entangled state as described in claim 1, which is expressed as follows: Among them, quantum bits 2, 4, 6, and 8 belong to the first communication party, 3, 5, 7, and 9 belong to the second communication party, and 1 belongs to the control communication party.

5. The method of bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel according to claim 1, characterized in that: In step (2), the first communication party and the second communication party follow the following protocol: if the single-qubit orthogonal basis measurement result of one communication party is |+>, then send a classical bit "0" to the other communication party, otherwise send a classical bit "1", if the Bell state measurement result of one communication party is |ψ + >,|ψ - >, Send classical bits "00", "01", "10", "11" to another communication party. In step (3), the communication party is controlled to follow the following protocol: if the measurement result of the single-qubit computation basis is |0>, then he sends the classical bit "0" to the first communication party and the second communication party, otherwise he sends the classical bit "1".

6. The method of bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel according to claim 1, characterized in that: In step (4), the first communication party and the second communication party respectively perform corresponding transformation operations on the quantum bits (3, 5) and (6, 8) according to the measurement results of the control communication party and the other party. j ,m,n,k,l,q and O r,s,t,x,y,q .

7. The method of bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel according to claim 1, characterized in that: In step (5), the first communication party and the second communication party first fix the quantum states of quantum bits a1 and b2 to and Next, two two-qubit controlled NOT gate operations are performed on the qubit pairs (6, a1) and (3, b2), where qubits 6 and 3 serve as control qubits, and qubits a1 and b2 serve as target qubits.

8. The method of bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel according to claim 7, characterized in that: The first communication party and the second communication party acquire the quantum state and The specific method is: if the measurement result of the first communication party in step (2) is Then a Hadamard gate operation H is performed on qubit a1, otherwise a Pauli-Hadamard gate composite operation σ is performed x H; If the measurement result of the second communication party in step (2) is Then a Hadamard gate operation H is performed on qubit b2, otherwise a Pauli-Hadamard gate composite operation σ is performed x H.

9. The method of bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel according to claim 1, characterized in that: After the operation is completed, the quantum states of the quantum qubit groups (6, a1, 8) and (3, b2, 5) are reconstructed as:

10. A method for bidirectionally controllable symmetric stealth transmission of two three-qubit target quantum states based on a nine-qubit entangled channel according to claims 1-9, characterized in that: The definitions of the various measurements and operations described are as follows, Single quantum bit computational basis measurement basis vector: {|0>,|1>}; Single-qubit orthogonal basis measurement basis vector: {|+>,|->}, where Bell state basis measurement basis vector: in, The expression of Hadamard gate operation H= is: The expression of the unit operation I is: I=|0><0|+|1><1|; Pauli operation σ x , σ y , σ z The expression of σ is: x =|0><1|+|1><0|,σ y =|0><1|-|1><0|,σ z =|0><0|-|1><1|; The expression of the two-qubit control Harman operation U is: in Quantum bit e is the control qubit, and qubit f is the target qubit; The expression of the two-qubit controlled NOT gate operation N is: Among them, quantum bit g is the control quantum bit, and quantum bit h is the target quantum bit.

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