CN111294204B - Method for preparing cluster state based on five-bit brown state - Google Patents
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Abstract
The invention discloses a method for preparing a four-bit cluster state based on a five-bit brown state. In the method, Alice, Bob and Charlie share a five-bit brown channel, wherein Alice is a sending party, Bob is a receiving party, and Charlie is a controlling party. Alice introduces two auxiliary particles to perform amplitude and phase measurement respectively after CNOT operation, informs Bob of the measurement result, and Charlie performs { |0>, |1> } measurement after agreeing to the measurement of Alice and Bob and sends the measurement result to Bob. Bob executes corresponding unitary operation according to the measurement result, and finally two auxiliary particles are introduced to execute the CNOT operation to obtain a four-bit cluster state. The invention has the beneficial effects that: 1. a method for preparing an arbitrary cluster state using a five-bit brown state is provided. 2. All the measurement modes adopted by the invention are two-bit measurement and CNOT operation, thereby greatly reducing the specific operation difficulty.
Description
Technical Field
The invention relates to the field of communication networks, in particular to a method for preparing cluster states based on a five-bit brown state.
Background
Quantum communication is an important branch of quantum informatics, and is an earlier field of research in quantum information. Quantum communication is the efficient transfer of information in quantum states as units of information. In quantum communication, besides the traditional classical channel, a quantum channel between communication parties needs to be established more mainly. What is called a quantum channel is in fact a quantum entanglement between communicating parties. The application of quantum entanglement in communication creates an incredible miracle of classical information theory, such as 'quantum dense coding' for transmitting classical bits by using a quantum channel, 'quantum invisible state' for transmitting quantum states by using a classical auxiliary method, and 'absolute safe quantum cryptography' required by information security transmission [1 ].
The quantum entanglement state is the quantum state which most commonly exists in a quantum mechanics multi-particle system or a multi-degree-of-freedom system but is very special. It is one of the wonderful characteristics of quantum mechanics, namely that the measurement result of one subsystem cannot be independent of the measurement parameters of other subsystems. In 1935 Einstein, Podolsky, Rosen published a short and very important article [2] first related to entanglement states, later called the paradox EPR. Schrodinger in the same year defined the concept of entanglement status in his famous article [3 ]. The proposal of entangled state prompts people to deeply discuss the traditional quantum mechanics, and the theory and oath related to entangled state are the main direction of the quantum mechanics development in recent decades. The entangled state plays an important role in understanding the basic concept of quantum mechanics. But the function of the quantum information is not only the same, and with the vigorous development of a new field of quantum information science, the quantum entanglement state gradually ascends the stage of the quantum information field and establishes the dominant position of the quantum information field. The quantum entangled state is used as a carrier of quantum communication and quantum computation, and is widely applied to the fields of quantum invisible state transfer, quantum key distribution, quantum dense coding, quantum computation and the like.
Remote preparation of quantum states (remote state preparation) is the successful realization of the transfer of a known quantum state based on classical information and entangled states. RSP is used to transfer a known state between sender Alice and receiver Bob. Bob obtains the target state by performing an appropriate single operation. In 2000, Lo 4, Pati 5 and Bennett 6 et al proposed schemes for the remote preparation of known quantum states. Stealth transmission schemes and remote fabrication schemes have many similarities, but the information of the quantum states to be transmitted in the former is unknown, which is quite different from the latter. In the remote state preparation scheme, it is a prerequisite that the sender knows the information of the quantum state to be transmitted, and is therefore also referred to as "quantum invisible transmission of a known state". Basic idea of remote state preparation: first, sender Alice and receiver Bob share the entangled resource, and Alice performs some classical information and local operations to achieve the transmission of a quantum state that is completely known to her but unknown to Bob. Seven-bit quantum channels are also commonly used for quantum transport. For example, Yang et al proposed an improved quantum proxy blind signature scheme based on controlled stealth states [7 ]. Lie sensitivity proposes an improved quantum stealth state scheme for a five-qubit unknown state with seven-qubit quantum channels [8 ]. Remote state preparation is an emerging subject, draws attention of various national scholars from the beginning, and makes great progress on theory and experiments nowadays. In theory, many schemes have been proposed. To date, RSP has gained increasing interest due to the lower consumption of qubit resources. Various RSP protocols have been proposed, such as deterministic RSP [9], federated RSP (JRSP) [10,11], Controlled RSP (CRSP) [12] - [17], forgetful RSP [18], low-entanglement RSP [19] and continuous variable RSP [20 ].
There are many current approaches to JRSP. In JRSP, several senders share knowledge of the readiness state. Each sender holds part of the information, the receiver has no information about the status. When all senders collaborate, the receiver can reconstruct the desired state by some manipulation of his own particles. For example, in 2015, Li proposed a JRSP [21] for a two-qubit equatorial state. 2016, King et al. A DJRSP scheme is proposed in which four qubit states are prepared as quantum channels through two GHZ states [22 ]. 2017, Fu et al. This idea is extended to implement the JRSP scheme of any four-qubit W-type entangled states by using two three-qubit GHZ states as quantum channels [23 ]. In 2017, Wang proposed bi-directional control joint remote status preparation by seven qubit entangled state [24 ]. In 2018, Xiao et al. A JRSP scheme is proposed in which single-quantum-site states are prepared by three-atom entangled GHZ-type states [25 ]. 2018, Liao et al. A JRSP scheme for any two-qubit state is proposed by cluster states [26 ].
Reference documents:
【1】 Suxiaoqin, Guo Guangliu quantum communication and quantum computing [ J ] Quantum electronics, 2004,21(6): 706-.
【2】Einstein A，PodolskyB，Rosen N.Can Description of Physical Reality be Considered Complete?[J].Phys.Rev.，1935，47：777—780.
【3】Schrodinger E.Die Gegenwartige Situation in derQuantenmechanik[J].NaturwissenSchaften，1935，23：807～812；823—828：844—849.
【4】Pati A K.Minimum classical bit for remote preparation and measurement of a qubit[J].Physical Review A,2000,63(63):94-98.
【5】Li X and Ghose S 2017 Int.J.Theor.Phys.56667–77
【6】J.-F.Li,J.-M.Liu,X.-L.Feng,and C.H.Oh,“Deterministic remote two-qubit state preparation in dissipative environments,”Quantum Inf.Process.,vol.15,no.5,pp.2155-2168,2016.
【7】Yang Y Y,Xie S C,Zhang J Z.An Improved Quantum Proxy Blind Signature Scheme Based on Genuine Seven-Qubit Entangled State[J].International Journal of Theoretical Physics,2017,56(7):2293-2302.
【8】Yang Y,Jiang M,Zhou L L.Improving the Teleportation Scheme of Five-Qubit State with a Seven-Qubit Quantum Channel[J].International Journal of Theoretical Physics,2018,57(11):3485-3491.
【9】B.An Nguyen,T.B.Cao,V.Don Nung,and J.Kim,“Remote state preparation with unit success probability,”Adv.Natural Sci.,Nanosci.Nanotechnol.,vol.2,p.035009,Jul.2011.
【10】Choudhury B S,Dhara A.Joint remote state preparation for two-qubit equatorial states.[J].Quantum Information Processing,2015,14(1):373-379.[11]Nguyen B A 2010 Opt.Commun.283 4113-17
【11】Zhang C Y,Bai M Q,Zhou S Q.Cyclic joint remote state preparation in noisy environment[J].Quantum Information Processing,2018,17(6):146.
【12】L.Huang and H.-X.Zhao,“Controlled remote state preparation of an arbitrary two-qubit state by using GHZ states,”Int.J.Theor.Phys.,vol.56,no.3,pp.678-682,2017.
【13】Chen X B,Ma S Y,Su Y,et al.Controlled remote state preparation of arbitrary two and three qubit states via the Brown state[J].Quantum Information Processing,2012,11(6):1653-1667.
【14】Kiktenko E O,Popov A A,Fedorov A K.Bidirectional imperfect quantum teleportation with a single Bell state[J].Physical Review A,2016,93(6):062305.
【15】Da Z,Zha X W,Duan Y J,et al.Deterministic Controlled Bidirectional Remote State Preparation Via a Six-qubit Maximally Entangled State[J].International Journal of Theoretical Physics,2016,55(1):440-446.
【16】Da Z,Zha X W,Duan Y J,et al.Deterministic Controlled Bidirectional Remote State Preparation Via a Six-qubit Maximally Entanged State[J].International Journal of Theoretical Physics,2016,55(1):440-446.
【17】Chen X B,Sun Y R,Xu G,et al.Controlled bidirectional remote preparation of three-qubit state[J].Quantum InformationProcessing,2017,16(10):244.
【18】Leung,D.W.,Show,P.W,“Oblivious remote state preparation,”Phys.Rev.Lett.,90,127905,2003.
【19】Devetak I,Berger T.Low-entanglement remote state preparation.[J].Physical Review Letters,2001,87(19):197901.
【20】Paris,M.G.A,Cola,M.,Bonifacio,R,“Remote state preparation and teleportation in phase space”J.Opt.B.5(3),247-50,2003.
【21】X.Li,S.Ghose,“Optimal joint remote state preparation of equatorial states,”Quantum Information Processing,14(12):4585-4592,2015.
【22】Wang H B,Zhou X Y and An X X,2016 International Journal of Theoretical Physics 553588-96
【23】Fu H,Ma P C,Chen G B,et al.Efficient schemes for deterministic joint remote preparation of an arbitrary four-qubit W-type entangled state[J].Pramana,2017,88(6):92.
【24】X.Y.Wang,Z.W.Mo,“Bidirectional Controlled Joint Remote State Preparation via a Seven-Qubit Entangled State,”International Journal of Theoretical Physics,56(4):1052-1058,2017.
【25】Xiao X Q,Yao F,Lin X,et al.Joint Remote State Preparation of a Single-Atom Qubit State via a GHZ Entangled State[J].International Journal of Theoretical Physics,2018,57(4):1132-1140.
【26】Liao Y M,Zhou P,Qin X C,et al.Efficient joint remote preparation of an arbitrary two-qubit state via cluster and cluster-type states[J].Quantum Information Processing,2014,13(3):615-627.
Disclosure of Invention
The invention aims to provide a method for preparing cluster states based on a five-bit brown state.
In order to solve the above technical problem, the present invention provides a method for preparing a cluster state based on a five-bit brown state, including:
alice, Bob and Charlie share a five-bit brown channel, wherein Alice is a sender, Bob is a receiver and Charlie is a controller. Firstly, Alice introduces two auxiliary particles and executes CNOT operation, secondly, Alice executes amplitude measurement again, selects a corresponding phase measurement base according to the result of the amplitude measurement to perform phase measurement, and finally sends the results of the two measurements to Bob, and Charlie executes { |0>, |1> } measurement and sends the measurement result to Bob after agreeing with the measurements of Alice and Bob. Bob executes unitary operation according to the measurement results of Alice and Charlie to restore the target state, and then introduces two auxiliary particles to execute CNOT operation to prepare an arbitrary cluster state. The complete process comprises the following steps:
the method comprises the following steps: forming channels
Alice, Bob and Charlie share a five-bit brown channel of the form:
where Alice possesses particles 1 and 2, Bob possesses particles 3 and 4, and Charlie possesses particle 5.
Alice introduces auxiliary particle |00>ABAnd performing a CNOT operation on the particle pairs (1, A) and (3, B), the overall system being of the form:
step two: amplitude and phase measurement
Alice performs amplitude and phase measurements on the particle pairs (1,2) and (a, B), respectively, as follows:
alice selects a set of orthogonal measurement bases { |% { | { (X) }i>；i∈{0,1,2,3}}：
The whole system can be decomposed into the following forms:
alice has 4 measurement results { chi0>,|χ1>,|χ2>，|χ3>}. Alice sends the measurement results to Bob, and in view of the measurement results, Alice selects the appropriate phase measurement basis for the second time
According to the form of the measurement basis, the whole system can be decomposed into the following form:
alice has 16 measurement results, which are as follows:
step three: controlling measurements
Charlie is the controlling party, and when Charlie agrees to Alice and Bob to perform the measurement, the Charlie performs { |0>, |1> } measurement and sends the measurement result to Bob.
Step four: restoring the target equivalent
And in the case that Charlie agrees to the measurement of Alice and Bob, Charlie and Alice send the measurement result to Bob, and Bob performs unitary operation according to the measurement result to restore the target equivalent value.
For example, the result of measurement is
Bob performs on particles 3 and 4
Operation to restore the target equivalent value to
Bob introduces two auxiliary particles |00>67Performing a CNOT operation with particles 3 and 4 as control qubits and particles 6 and 7 as target qubits, while performing a CZ operation on the pair of particles (6, 7) to prepare a four-bit cluster state
The invention has the beneficial effects that:
1. a method for preparing an arbitrary cluster state using a five-bit brown state is provided.
2. All the measurement modes adopted by the invention are two-bit measurement and CNOT operation, thereby greatly reducing the specific operation difficulty.
Drawings
FIG. 1 is a flow chart of the method for preparing cluster states based on a five-bit brown state according to the present invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
The technical terms of the invention explain:
1. pauli array
Some unitary matrices, also known as Pauli matrices, are also used in the present invention. The specific form is as follows:
2. CNOT operations
The CNOT operation is a not gate operation, and the two qubits are a control bit and a target bit, respectively. When the control bit is |0>, the target bit is unchanged; when the control bit is |1>, the target bit is inverted. The matrix form that the CNOT operation acts on the qubit pairs is as follows:
3. CZ operation
The CZ operation is a control Z operation, and the two qubits are a control bit and a target bit respectively. When the control bit is |0>, the target bit is unchanged; when the control bit is |1>, the target bit sign is inverted. The matrix form of the CZ operation's effect on qubit pairs is as follows:
the first embodiment is as follows: a scheme for preparing cluster state based on five-bit brown state, which takes the preparation target state as
For example, the method specifically comprises the following steps:
the method comprises the following steps: forming channels
Alice, Bob and Charlie share a five-bit brown channel of the form:
where Alice possesses particles 1 and 2, Bob possesses particles 3 and 4, and Charlie possesses particle 5.
Alice introduces auxiliary particle |00>ABAnd performing a CNOT operation on the particle pairs (1, A) and (3, B), the overall system being of the form:
step two: amplitude and phase measurement
Alice performs amplitude and phase measurements on the particle pairs (1,2) and (a, B), respectively, as follows:
alice selects a set of orthogonal measurement bases { |% { | { (X) }i>；i∈{0,1,2,3}}：
The whole system can be decomposed into the following forms:
alice has 4 measurement results { |% { | { (X) }0>,|χ1>,|χ2>，|χ3>}. Alice sends the measurement results to Bob, and in view of the measurement results, Alice selects the appropriate phase measurement basis for the second time
According to the form of the measurement basis, the whole system can be decomposed into the following form:
alice has 16 measurement results, which are as follows:
step three: controlling measurements
Charlie is the controlling party, and when Charlie agrees to Alice and Bob to perform the measurement, the Charlie performs { |0>, |1> } measurement and sends the measurement result to Bob.
Step four: restoring the target equivalent
And in the case that Charlie agrees to the measurement of Alice and Bob, Charlie and Alice send the measurement result to Bob, and Bob performs unitary operation according to the measurement result to restore the target equivalent value.
For example, the result of measurement is
Bob performs on particles 3 and 4
Operation to restore the target equivalent value to
Bob introduces two auxiliary particles |00>67Performing a CNOT operation with particles 3 and 4 as control qubits and particles 6 and 7 as target qubits, while performing a CZ operation on the pair of particles (6, 7) to prepare a four-bit cluster state
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (1)
1. A method for preparing cluster state based on five-bit brown state is characterized by comprising the following steps:
alice, Bob and Charlie share a five-bit brown channel, wherein Alice is a sender, Bob is a receiver, and Charlie is a controller; firstly, introducing two auxiliary particles by Alice and executing CNOT operation, secondly, performing amplitude measurement by Alice, selecting a corresponding phase measurement base according to the result of the amplitude measurement to perform phase measurement, and finally sending the results of the two measurements to Bob, wherein Charlie executes { |0>, |1> } measurement after the Alice and the Bob are agreed to perform the measurement and sends the measurement result to the Bob; bob executes unitary operation according to the measurement results of Alice and Charlie to restore the target state, and then introduces two auxiliary particles to execute CNOT operation to prepare an arbitrary cluster state;
the complete process comprises the following steps:
the method comprises the following steps: forming channels
Alice, Bob and Charlie share a five-bit brown channel;
alice introduces auxiliary particle |00>ABAnd performing a CNOT operation on the particle pairs (1, A) and (3, B);
step two: amplitude and phase measurement
Alice performs amplitude and phase measurements on the particle pairs (1,2) and (a, B), respectively, as follows:
alice selects a set of orthogonal measurement bases { |% { | { (X) }i>；i∈{0,1,2,3}}：
The whole system can be decomposed into the following forms:
alice has 4 measurement results { |% { | { (X) }0>,|χ1>,|χ2>，|χ3}; alice sends the measurement to Bob and, taking into account the measurement, Alice selects the phase measurement basis a second time
According to the form of the measurement basis, the whole system can be decomposed into the following form:
step three: controlling measurements
Charlie is a control party, and when Charlie agrees to Alice and Bob to perform measurement, Charlie executes { |0>, |1> } measurement and sends the measurement result to Bob;
step four: restoring the target equivalent
Under the condition that Charlie agrees to measurement by Alice and Bob, Charlie and Alice send the measurement result to Bob, and Bob executes unitary operation according to the measurement result to recover the target equivalent value;
in the first step, the form of the five-bit brown channel shared by Alice, Bob and Charlie is as follows:
where Alice possesses particles 1 and 2, Bob possesses particles 3 and 4, and Charlie possesses particle 5;
in step one, after the CNOT operation is performed, the form of the whole system is as follows:
in the second step, Alice selects the phase measurement basis for the second time
The method comprises the following specific steps:
in the second step, Alice has 16 measurement results, which are as follows:
in step three, the measurement result is
Then Bob executes on particles 3 and 4
Operation to restore the target equivalent value to
Bob introduces two auxiliary particles |00>67Performing a CNOT operation with particles 3 and 4 as control qubits and particles 6 and 7 as target qubits, while performing a CZ operation on the pair of particles (6, 7) to prepare a four-bit cluster state
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