Method for splitting any state of one or two quantum bits in four directions
By introducing a four-sided architecture into quantum information splitting, using six-qubit cluster states and specific quantum operations, the problems of high operation difficulty and low transmission efficiency in the existing trilateral quantum information splitting methods are solved, and more efficient and secure quantum information transmission is achieved.
Patent Information
- Application Number
- CN202510348937.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-24
- Publication Date
- 2025-05-02
AI Technical Summary
Most of the existing quantum information splitting methods involve only three parties, which leads to high operational difficulty and low transmission efficiency, limiting its application in future quantum networks.
A method of splitting one or two quantum bits in four directions is proposed. The splitting and reconstruction of quantum states is achieved by sharing the six quantum bit cluster states as quantum channels by four legal communication parties (one information sender, two information supervisors and one information receiver).
It realizes quantum information splitting with low operation difficulty and high transmission efficiency, enhances the security and reliability of information transmission, and is suitable for applications in multi-party quantum networks.
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Abstract
Description
Technical Field
[0001] The present invention relates to the field of quantum communication technology, and more specifically, to a method for four-way splitting of one or two quantum bit arbitrary states. Background Art
[0002] In the past three decades, the combination of quantum mechanics, information science, and computer science has produced a new discipline called quantum information science, which includes quantum communication and quantum computing. Quantum entanglement plays an important role in both quantum communication and quantum computing. It is a unique feature of quantum mechanics and has no corresponding classical physical phenomenon. There are non-local correlations between entangled quantum bits. Measuring and manipulating quantum entangled resources can obtain and change quantum information, thereby realizing many quantum tasks, such as quantum key distribution, quantum secure direct communication, quantum operation sharing, quantum identity authentication, quantum remote state preparation, etc.
[0003] It is based on quantum entanglement and the necessary local quantum operations and classical communication that Bennett et al. introduced the concept of quantum teleportation (QST) in 1993. Using QST technology, an arbitrary unknown quantum state can be remotely transmitted from one quantum bit to another quantum bit without directly transmitting any physical carrier. QST is an effective way to achieve long-distance transmission of quantum information and remote configuration of quantum resources, and it has been widely studied in both experiments and theory.
[0004] In the early QST technology, only two legitimate users were involved, namely a sender and a receiver of quantum confidential information. However, a single receiver lacks necessary constraints and may endanger information security in some important situations. For example, if the single receiver in the military is a spy, he may leak secrets or arbitrarily tamper with the received information and misreport military intelligence or combat instructions. Therefore, from the perspective of information security, Karlsson and Bournane proposed a new mode of quantum teleportation in 1998, namely quantum information splitting (QIS), sometimes also called quantum confidential sharing. Quantum information splitting technology involves three or more legitimate communication users, including a sender of quantum information and several receivers of quantum information. The information sender splits the quantum confidential information to be sent into several fragments through local operations and measurements and transmits them invisible to the quantum bits of all information receivers. Therefore, without the help of other receivers, no single receiver can obtain the complete confidential information. In other words, only with the joint supervision and help of all receivers can they extract the complete target quantum information as a whole. Due to this feature of quantum information splitting technology, it has many potential application scenarios in future quantum networks. For example, the quantum information to be transmitted has important commercial value or involves important military secrets, and the sender does not fully trust a single receiver, fearing that she / he will leak or tamper with the confidential quantum information. In this case, with the supervision and constraints of other controlling parties, the security of information transmission is increased, and many potential risks are effectively avoided. Therefore, QIS has received a lot of attention so far.
[0005] However, since QIS requires the use of multi-qubit entangled resources as quantum channels, the more participants involved, the greater the amount of quantum information to be transmitted, the greater the number of qubits of entangled resources, the more complex the entangled structure distribution, and the greater the difficulty and intensity of the necessary quantum measurements and quantum operations used to complete the QIS task. Because of this, most of the existing quantum information splitting methods only involve three parties, that is, there is only one supervisory party and there are defects such as high operational difficulty and low transmission efficiency. This has limited the application scenarios of QIS in future quantum networks to a certain extent and affected the practical application process of QIS. Summary of the invention
[0006] The present invention provides a method for four-party splitting of one or two quantum bit arbitrary states, which solves the technical problem that most of the existing quantum information splitting methods in the relevant technology only involve three parties, that is, there is only one supervisor and the quantum states to be transmitted are mostly single quantum bit states, which affects the practical application process of QIS.
[0007] The present invention provides a method for four-way splitting of one or two quantum bits in arbitrary states, which has the advantages of low operation difficulty and high transmission efficiency, and comprises the following steps:
[0008] Step S_1, four legal communication parties include an information sender, two information supervisors and an information receiver. The four parties share a six-qubit cluster state as a quantum channel, where qubits 1 and 6 belong to the information sender, qubits 2 and 5 belong to the first information supervisor and the second information supervisor respectively, and qubits 3 and 4 belong to the information receiver; the information sender has two entangled qubits x and y, and any unknown state of the qubits is used as the target quantum state;
[0009] Step S_2, the information sender performs two two-qubit controlled NOT gate operations on its qubit pairs (x, 1) and (y, 6), where qubits x and y are respectively used as control qubits, and qubits 1 and 6 are respectively used as target qubits;
[0010] Step S_3, the information sender uses the single-qubit computing basis {|0>,|1>} to measure its qubits 1 and 6, and uses the single-qubit orthogonal basis {|+>,|->} to measure its qubits x and y, and then uses the classical channel to send the measurement results to the information receiver;
[0011] Step S_4, the first information supervisor and the second information supervisor use the single quantum bit orthogonal basis {|+>,|->} to measure their quantum bits 2 and 5 respectively, and then send the measurement results to the information receiver through the classical channel;
[0012] In step S_5, the information receiver first performs a two-qubit controlled phase gate operation on its quantum bit pair (3, 4), and then performs corresponding conversion operations on the quantum bit pair (3, 4) to restore the target quantum state of the information sender according to the measurement result information sent by the information sender, the first information supervisor and the second information supervisor.
[0013] Furthermore, the six-qubit cluster state is in the form of:
[0014]
[0015] Furthermore, the form of the arbitrary target quantum state of the two quantum bits is:
[0016]
[0017] Among them, θ m,n ∈(0,2π] and α m,n (m,n=0,1) are all real numbers and satisfy These parameter information are unknown to anyone, including the sender of the information.
[0018] Furthermore, the two-qubit controlled NOT gate operation is defined as:
[0019]
[0020] Where: (0,0) =|0><0|+|1><1| is a unit operation, σ (0,1) =|0><1|+|1><0| represents a Pauli operation. The other two Pauli operations in the present invention are respectively represented by σ (1,0) =|0><1|-|1><0| and σ (1,1) =|0><0|-|1><1|.
[0021] Furthermore, the relationship between the single-qubit orthogonal basis and the single-qubit computational basis is:
[0022]
[0023] Furthermore, the four communicating parties agree in advance that the classical bit "0" represents the single quantum bit computing basis measurement result |0> or the single quantum bit orthogonal basis measurement result |+>, and the classical bit "1" represents the single quantum bit computing basis measurement result |1> or the single quantum bit orthogonal basis measurement result |->.
[0024] Furthermore, the first information supervisor and the second information supervisor play the role of controlling, supervising and assisting the information receiver in reconstructing the target quantum state in the quantum information splitting task. After step S_3, if any of the two supervisors disagrees to carry out this task, the subsequent steps are terminated immediately.
[0025] Furthermore, the two-qubit controlled phase gate operator is expressed as:
[0026]
[0027] Furthermore, the two-qubit conversion operation is composed of a unit operation and a Pauli operation set {σ (0,0) ,σ (0,1) ,σ (1,0) ,σ (1,1)} is composed of the two operations in .
[0028] The present invention further provides a system for implementing quantum state information transmission processing, which is used to execute the aforementioned method of four-way splitting one or two quantum bit arbitrary states.
[0029] The beneficial effects of the present invention are as follows: Based on the six-qubit cluster state as a quantum channel, the present invention proposes a new method for quantum information splitting by rationally allocating and arranging entangled resources and using a series of quantum measurements and quantum operations that have been experimentally realized. The method can realize the information splitting and reconstruction of two-qubit arbitrary target states by four communication parties (a quantum information sender, two information supervisors and one information receiver). Compared with the existing quantum information splitting technology, the present invention has the advantages of more participants, high transmission efficiency and strong feasibility. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Figure 1 It is a technical roadmap of a method for four-way splitting of one or two quantum bits in arbitrary states of the present invention;
[0031] Figure 2 is the quantum resource population diagram of the present invention;
[0032] Figure 3 The quantum operation process of the present invention is Figure 1 ;
[0033] Figure 4 The quantum operation process of the present invention is Figure 2 ;
[0034] Figure 5 The quantum operation process of the present invention is Figure 3 ;
[0035] Figure 6 The quantum operation process of the present invention is Figure 4 .
[0036] Figure 2-6 The solid sphere in the middle represents the quantum bit, the rounded square represents the territory of the participant, the solid square represents the single quantum computing basis measurement, the dotted square represents the single quantum bit orthogonal basis measurement, the solid ellipse represents the two-qubit controlled NOT gate operation, the dotted ellipse represents the two-qubit controlled phase gate operation, the solid circle represents the recovery operation, the dotted straight line represents the classical channel, and their arrows represent the propagation direction of classical information. DETAILED DESCRIPTION
[0037] 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.
[0038] At least one embodiment of the present invention discloses a method for four-way splitting of one or two quantum bit arbitrary states, including five steps, which are described in detail below with reference to the accompanying drawings:
[0039] Step S_1, the four legal communication parties include an information sender and three information receiving agents, named Anne, Bob, Chris and David, where Anne is the information sender, and Bob, Chris and David are her three information agents. At the beginning, Anne has two entangled quantum bits x and y, whose quantum state information is unknown to anyone, including Anne herself. Without loss of generality, any unknown state of the two quantum bits can be expressed as:
[0040]
[0041] Here, θ m,n ∈(0,2π] and α m,n (m,n=0,1) are all real numbers and satisfy In this invention, for the convenience of description, we refer to the two-qubit arbitrary unknown state Anne wants to call the target quantum state However, Anne cannot fully trust any of her three agents individually, unless the three agents as a whole can supervise and constrain each other. In this case, Anne can send the target quantum state The information contained is divided into three parts and transmitted invisible to her three agents Bob, Chris and David. If and only if Bob, Chris and David help each other and cooperate with each other, they can finally reconstruct the target quantum state transmitted by Anne. After negotiation, the three agents decided that Bob and Chris would jointly supervise and help David reconstruct the target quantum state sent by Anne on his quantum bit. In order to achieve the above purpose, a six-qubit cluster state is used to construct a quantum channel between the four communicating parties. The specific expression of the six-qubit cluster state is:
[0042]
[0043] Among them, qubits 1 and 6 belong to Anne, qubits 2 and 5 belong to Bob and Chris respectively, and qubits 3 and 4 belong to David. [See Figure 2 ]
[0044] Step S_2: Anne performs two two-qubit controlled NOT gate operations on her qubit pairs (x, 1) and (y, 6), where qubits x and y are used as control qubits, and qubits 1 and 6 are used as target qubits. [See Figure 3 ]
[0045] In the present invention, the control NOT gate operation is defined as:
[0046]
[0047] Here, σ (0,0) =|0><0|+|1><1| is a unit operation, σ (0,1) =|0><1|+|1><0| represents a Pauli operation. By the way, there are two more Pauli operations that will be used in subsequent steps. Their quantum operators are σ (1,0) =|0><1|-|1><0| and σ (1,1) =|0><0|-|1><1|. Anne's two control NOT gate operations change the quantum state of the entire physical system to:
[0048]
[0049] here,
[0050]
[0051] Step S_3: Anne first measures her qubits 1 and 6 using the single-qubit computational basis {|0>,|1>}, and measures her qubits x and y using the single-qubit orthogonal basis {|+>,|->}, and then sends the measurement results to David using the classical channel. [See Figure 4 ]
[0052] In the present invention, the relationship between the single-qubit orthogonal basis and the single-qubit computational basis is After Anne's measurement, the remaining qubits (2, 3, 4, and 5) collapse with equal probability into one of the following 16 possible quantum states.
[0053]
[0054] In the above formula, the symbol ± x and ± y The orthogonal basis measurement results corresponding to quantum bits x and y respectively, and their superposition satisfies the multiplication rule.
[0055] Anne and her three agents, Bob, Chris and David, have reached an agreement in advance that the classical bit "0" represents the single-qubit computational basis measurement result |0> or the single-qubit orthogonal basis measurement result |+>, while the classical bit "1" represents the single-qubit computational basis measurement result |1〉 or the single-qubit orthogonal basis measurement result |->. Therefore, based on the measurement results of qubits 1, 6, x and y, Anne sends a 4-bit classical information string (c1, c6, c x ,c y ). For example, if Anne's measurement result in step S_2 is |0>1, |1>6, |-〉 x and|+〉 y , then she sends a 4-bit classical information string (0,1,1,0) to David.
[0056] Step S_4: If Bob and Chris do not agree to let David receive the target quantum state sent by Anne, the communication ends here. If they agree and are willing to help, Bob and Chris first use the single-qubit orthogonal basis to measure their qubits 2 and 5 respectively, and then send 1 bit of classical information (c2) and (c5) to David respectively to announce their measurement results to David. [See Figure 5 ]
[0057] Obviously, Bob and Chris's measurements will further cause the remaining qubit pair (3, 4) to collapse into one of 64 possible situations with equal probability. For example, suppose in step S_3, Anne's measurement result is |1〉1, |0〉6, |+〉 x and |-> y , then in step S_3 the quantum states of the remaining qubits (2, 3, 4, and 5) will collapse to:
[0058]
[0059] In fact, in the single-qubit orthogonal basis framework, the above formula can also be rewritten as:
[0060]
[0061] in,
[0062]
[0063] Further assume that in this step, the measurement results of Bob and Chris are |+>2 and |->5 respectively, then the remaining qubit pair (3,4) collapses to
[0064]
[0065] The CS(3,4) column in Table 1 lists the corresponding collapsed states of the remaining quantum bit pairs (3,4) in all possible cases in this step.
[0066] Step S_5: David first performs a two-qubit controlled phase gate operation on his qubit pair (3,4), and then performs a corresponding conversion operation to restore the target quantum state transmitted by Anne. [See Figure 6 ]
[0067] In the present invention, the two-qubit controlled phase gate operator can be expressed as:
[0068]
[0069] After executing the two-qubit controlled phase gate operation Afterwards, based on the measurement results of Anne, Bob, and Chris, David selects a suitable conversion operation to act on his qubit pair (3,4). The TO column in Table 1 lists the specific forms of the corresponding conversion operations in various cases. For example, suppose Anne's measurement result is |0>1|1>6|-> x |+> y , the single-qubit orthogonal basis measurement results of Bob and Chris are |->2 and |+>5 respectively, then the remaining qubit pair (3,4) in step S_4 collapses to:
[0070]
[0071] In this case, Bob's conversion operation is After the conversion operation is performed, the quantum state of the quantum bit pair (3,4) finally evolves to
[0072]
[0073] From the above formula, we can see that Anne's two-qubit arbitrary target state has now been reconstructed on Bob's qubit pair (3,4). Calculations show that in any case, using the corresponding transformation operations listed in Table 1, the quantum state of Bob's qubit pair (3,4) will eventually evolve to In other words, the invention has a 100 percent chance of successfully transmitting the target quantum state.
[0074] Table 1: The collapsed state of the quantum bit pair (3,4) corresponding to various measurement results and the specific form of the corresponding conversion operation.
[0075]
[0076]
[0077]
[0078]
[0079]
[0080]
[0081]
[0082]
[0083] In the table, AMR represents Anne's measurement result, BMR represents Bob's measurement result, CMR represents Chris's measurement result, CS(3,4) represents the collapsed state of the quantum bit pair (3,4) after step S_4 is executed, and TO represents the conversion operation.
[0084] The present invention will be further described below in conjunction with performance analysis.
[0085] First of all, the quantum information splitting method proposed in the present invention has achieved an important breakthrough in the communication mode. It innovatively constructs a quantum communication architecture involving four parties, specifically including an information sender, two information supervisors and an information receiver. Compared with the prior art, most of the current quantum information splitting schemes only support a communication mode involving three parties (i.e., a single information supervisory party structure). The significant advantage of the present invention is that by introducing a second information supervisor, an additional layer of security protection mechanism is constructed on the system architecture. This dual supervision mechanism not only enhances the overall security of the system, but also significantly improves the reliability and anti-attack capability of information transmission. Both theoretical analysis and experimental verification show that compared with the traditional three-party quantum information splitting scheme, the four-party architecture of the present invention has obvious advantages in security, and provides a new technical path for the security protection of quantum communications.
[0086] Secondly, the present invention shows significant advantages in information transmission efficiency. The information transmission efficiency of quantum information splitting can be calculated by the following formula:
[0087]
[0088] Among them, q t The number of bits representing the target quantum state; q u represents the number of bits of quantum resources; c t Indicates the number of bits used in classical communication. In the embodiment of the present invention, the target quantum state is an arbitrary entangled state of two quantum bits. The quantum entanglement resource used is a six-qubit cluster state The information sender and the two information supervisors each sent a 4-bit classical information string (c1, c6, c x ,c y ) and two single-bit classical information (c2) and (c5), namely q t =2,q u =6, c t =6, therefore, the information transmission efficiency of the present invention is This efficiency is significantly higher than the transmission efficiency of general quantum information splitting schemes.
[0089] In addition, the present invention also shows outstanding technical advantages at the experimental implementation level. The necessary quantum operations used are limited to Pauli operations, single-qubit measurements, two-qubit controlled NOT gate operations, and controlled phase gate operations, which are all conventional operations in quantum information processing and have been widely implemented in various quantum physics systems, including ion trap systems, cavity quantum electrodynamics systems, and optical systems. Therefore, the experimental feasibility of the present invention is strong. However, existing quantum information splitting schemes usually rely on complex operations such as multi-qubit entangled state measurements, which currently still face great challenges in experimental implementation.
[0090] In the research work on splitting two-qubit arbitrary target quantum states, the scheme proposed by Yang et al. using five-qubit cluster states and Bell states as quantum channels [Int. J. Theor. Phys. 59: 187-199 (2014)] is highly representative at home and abroad. We refer to their scheme as the YLLC-QIS scheme. Table 2 lists in detail the comparison of the main performances of the present invention and the YLLC-QIS scheme.
[0091]
[0092] It can be intuitively seen from Table 2 that compared with the currently more advanced YLLC-QIS scheme, the present invention exhibits significant advantages in many aspects: first, the quantum resources (6qubits) and classical resources (6cbits) required by the present invention are both less than those of the YLLC-QIS scheme (7qubits and 7cbits); second, the information transmission efficiency of the present invention reaches 16.67%, which is higher than the 14.29% of the YLLC-QIS scheme; third, in terms of quantum measurement, the present invention only requires single quantum bit measurement (SQM), while the YLLC-QIS scheme requires complex Bell state basis measurement (BSM) and three-qubit GHZ state basis measurement (TGSM), which makes the experimental implementation of the present invention simpler and more feasible; finally, the present invention is applicable to four-party quantum information splitting while the YLLC-QIS scheme is only applicable to three-party quantum information splitting, that is, the present invention has a dual supervision mechanism while the YLLC-QIS scheme only has a single supervision mechanism, that is, the present invention has higher security in terms of information confidentiality. Obviously, the present invention is superior to the YLLC-QIS scheme in terms of quantum resource and classical resource consumption, information transmission efficiency, necessary quantum operation complexity, experimental feasibility, and information confidentiality and security.
[0093] In summary, through the rational layout and precise manipulation of quantum resources, the method of four-way splitting of one or two quantum bits to any target quantum state proposed in the present invention has achieved significant breakthroughs in multiple performance aspects, such as reducing the consumption of quantum resources and classical resources and the difficulty of experimental operation, improving the efficiency of information transmission and the security of information confidentiality, and providing a more feasible and efficient technical path for the practical application of quantum information splitting.
[0094] 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 four-way splitting of one or two quantum bit arbitrary states, characterized in that: The following steps are involved: Step S_1, four legal communication parties include an information sender, two information supervisors and an information receiver. The four parties share a six-qubit cluster state as a quantum channel, where qubits 1 and 6 belong to the information sender, qubits 2 and 5 belong to the first information supervisor and the second information supervisor respectively, and qubits 3 and 4 belong to the information receiver; the information sender has two entangled qubits x and y, and any unknown state of the qubits is used as the target quantum state; Step S_2, the information sender performs two two-qubit controlled NOT gate operations on its qubit pairs (x, 1) and (y, 6), where qubits x and y are respectively used as control qubits, and qubits 1 and 6 are respectively used as target qubits; Step S_3, the information sender uses the single-qubit computing basis {|0,|1} to measure its qubits 1 and 6, and uses the single-qubit orthogonal basis {|+,|-} to measure its qubits x and y, and then uses the classical channel to send the measurement results to the information receiver; Step S_4, the first information supervisor and the second information supervisor use the single quantum bit orthogonal basis {|+,|-} to measure their quantum bits 2 and 5 respectively, and then send the measurement results to the information receiver through the classical channel; In step S_5, the information receiver first performs a two-qubit controlled phase gate operation on its quantum bit pair (3, 4), and then performs corresponding conversion operations on the quantum bit pair (3, 4) to restore the target quantum state of the information sender according to the measurement result information sent by the information sender, the first information supervisor and the second information supervisor.
2. A method for tetragonal splitting of one or two quantum bit arbitrary states according to claim 1, characterized in that: The specific form of the six-qubit cluster state in step S_1 is:
3. A method for tetragonal splitting of one or two quantum bit arbitrary states according to claim 1, characterized in that: The form of the arbitrary target quantum state of the two quantum bits in step S_1 is: Among them, θ m,n ∈(0,2π] and αm,n(m,n=0,1) are both real numbers and satisfy 4. A method for tetragonal splitting of one or two quantum bit arbitrary states according to claim 1, characterized in that: The two-qubit controlled NOT gate operation in step S_2 is defined as: Among them, σ (0,0) =00+11 is a unit operation, σ (0,1) =01+10 represents a Pauli operation. In addition, the quantum operators of the other two Pauli operations involved in the present invention are σ (1,0) =|01|-|10| and σ (1,1) =|00|-|11|.
5. A method for tetragonal splitting of one or two quantum bit arbitrary states according to claim 1, characterized in that: The relationship between the single-qubit orthogonal basis and the single-qubit computational basis in step S_3 is:
6. A method for tetragonal splitting of one or two quantum bit arbitrary states according to claim 1, characterized in that: The correspondence between the single quantum bit measurement results and the classical information bits in steps S_3 and S_4 is: the classical information bit "0" represents the single quantum bit calculation basis measurement result |0 or the single quantum bit orthogonal basis measurement result |+, and the classical information bit "1" represents the single quantum bit calculation basis measurement result |1 or the single quantum bit orthogonal basis measurement result |-.
7. A method for tetragonal splitting of one or two quantum bit arbitrary states according to claim 1, characterized in that: The two-qubit controlled phase gate operator in step S_5 is expressed as:
8. A method for tetragonal splitting of one or two quantum bit arbitrary states according to claim 1, characterized in that: The two-qubit conversion operation described in step S_5 is composed of a unit operation and two operations in the Pauli operation set {σ(0,0),σ(0,1),σ(1,0),σ(1,1)}.
9. A system for implementing quantum state information transmission and processing, characterized in that: It is used to execute the method of tetragonally splitting one or two quantum bit arbitrary states as described in any one of claims 1-8.