CN109861751B - Remote extension method for realizing cluster state based on maximum entanglement Bell state - Google Patents
Remote extension method for realizing cluster state based on maximum entanglement Bell state Download PDFInfo
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Abstract
The invention discloses a remote expansion method for realizing cluster state based on maximum entanglement Bell state. The center node Alice enables the edge node Charlie to be assisted by the intermediate nodet(t ═ 1,2,3,4) enables remote extension of the cluster state. The method comprises the following steps: (1) constructing a distance extension path: the central node Alice holds a set of partially entangled cluster states | C >1234On the transmission path, the center node Alice and the edge node CharlietAnd (t ═ 1,2,3 and 4) and the intermediate nodes are mutually connected in pairs, and share a maximum entanglement Bell state with each other. The invention has the beneficial effects that: 1. the measurement results of the intermediate nodes can be transmitted simultaneously, so that the efficiency of information transmission is improved, and the requirement of constructing a complex quantum communication network can be met. 2. All the measurement modes adopted by the invention are Bell-based measurement and single-bit measurement, and the specific operation difficulty is greatly reduced. 3. The invention expands the communication distance, and enables the edge nodes not directly sharing the quantum entanglement pairs to realize quantum communication.
Description
Technical Field
The invention relates to the technical field of communication networks, in particular to a remote expansion method for realizing cluster state based on maximum entanglement Bell state.
Background
Quantum informatics has the characteristics of quantum characteristics and traditional classical information science, is a combined subject of quantum mechanics and traditional classical information science, and is a new subject applied to classical information science on the basis of quantum mechanics. Although the idea of quantum theory has been proposed for over a hundred years, the application of information in quantum mechanics has been only for decades, and the development time of quantum information is not long, but the development is extremely fast. Quantum informatics are different from classical informatics, and in the process of carrying out quantization on information, due to quantum characteristics, quantum states have entanglement, unclonability and superposition, so that when the information is transmitted, the capacity and safety carried by the information break through the limit in the conventional classical information transmission. Due to the unprecedented advantages of quantum informatics, quantum informatics have great breakthrough in theory and experiment, open up a new path for information transmission, and have a new mode. Subsequently, quantum informatics became a focus of research [1-5 ]. The research direction of quantum informatics includes quantum cryptography, quantum computing, quantum communication, quantum measurement and the like. As an important branch of quantum informatics, quantum communication mainly includes quantum invisible state transfer, quantum cryptography communication, quantum dense encoding, and the like.
Quantum entanglement is an indispensable physical resource in quantum communication. Quantum entanglement exists in a multi-particle system and a multi-degree-of-freedom system in quantum theory, and is unique in that one subsystem cannot be independently measured from other systems, namely if one subsystem in an entangled state is measured, other subsystems are influenced by the measurement and are changed. For example, if there are two electrons with the same velocity but opposite directions of motion, one of them is moved to south and the other to north, the two electrons will remain in a certain relationship even if they are far apart. Due to the characteristics, in 1935, Einstein, Podolsky, Rosen et al questioned the completeness of quantum mechanics, and verified by experiments, the experiment was regarded as an paradox, and quantum entanglement is involved, and the experimental negative-positive error verifies the non-local relevance of quantum entanglement. And in the same year, the first time,an "entangled state" is proposed. If the quantum state has an entangled property, it is called an "entangled state". The entangled state may be not only a pure state but also a mixed state.
For example, Bell state and GHZ (Greenberger-Home-Zeilinger) state [6], Brown state [7], W state [8], etc. since the cluster state, GHZ state, Bell state can be mutually transformed when the system is in a two-particle or three-particle system in the maximum entangled state, but the GHZ state and cluster state cannot be mutually transformed when the system is in a quantum state of more than three particles, the cluster state at this time has the characteristics of GHZ state and W state [9], and has been proved to have stronger capability of resisting decoherence [10], maximum connectivity and persistent entanglement than the GHZ state. At present, physics researchers have conducted extensive research on cluster states theoretically and experimentally and achieved remarkable results, and document [12] successfully realizes the preparation of four-photon cluster states and proves the feasibility of one-dimensional quantum computation; document [13] proposes the preparation of four-bit cluster states in cavity quantum electrodynamics and ion trap systems; in document [20], a scheme for remotely preparing 4 particle cluster states using 4 EPR pairs as quantum channels is proposed; document [21] proposes a remote preparation scheme for realizing 4 particle cluster states by using one EPR pair in combination with 2 3 particle GHz states as quantum channels. Because the Cluster state is important in the field of quantum information, the research on the Cluster state is of great significance.
Reference to the literature
[1] Phase sensitivity, plum spike, progress of fundamental research of quantum information physics [ J ]. china science, 2012,42(11):11761184.
[2]BennetCH,DiVincenzoDP.Quantuminformationandcomputation.Nature,2000,404(6775):247-255.
[3] Zulinling, Quantum Security direct communication based on multidimensional, multiple particle Quantum channels [ D ]. Suzhou: university of suzhou, 2009.
[4] Leaf euphorbia, preparation of high-dimensional quantum entanglement state and application in quantum communication [ D ]. mansion: university of chinese, 2013.
[5] Quantum invisible state-transfer technology research in quantum communication [ D ]. north Hu: university of science and technology in china, 2007.
[6]DAI H Y,CHEN P X,LIANG L M,et al.Classical communication cost andremote preparation of the four-particle GHZ class state[J].Physics Letters A,2006,355(4):285–288.
[7]LUO M X,PENG J Y,MO Z W.Joint remote preparation of an arbitraryfive-qubit brown state[J].International Journal of Theoretical Physics,2013,52(2):644–653.
[8]WANG D,HU Y D,WANG Z Q,et al.Efficient and faithful remotepreparation of arbitrary three-and four-particle W-class entangled states[J].Quantum Information Processing,2015,14(6):2135–2151
[9]Nie Y Y,LI Y H,Wang A S.Semi-quantuminformation splitting usingGHZ-type states[J].Quantum Information Processing,2013,12(1):437—448.
[10]Dür W,Briegel H J.Stability of macroscopic entanglement underdecoherence[J].Physical Review Letters,2004,92(18):180403.
[11]BRIEGEL H J,RAUSSENDORF R.Persistent entanglement in arrays ofinteracting particles[J].Physical Review Letters,2001,86(5):1–4
[12]ZOU X B,MATHIS W.Generating a four-photon polarization entangledcluster state[J].Physical Review A,2005,71(3):309–315.
[13]ZHENG X J,XU H,FANG Maofa,et al.Preparation of the four-qubitcluster states in cavity QED and the trapped-ion system[J].ChinesePhysics B,2010,19(3):034207
[14]Ma Pengcheng,Zhan Youbang.Scheme for remotely preparing a four-partical emtangled cluster-type state[J].Optics communication,2010,283(12):2640-2643.
[15]Ma Songya,Chen Xiubo,Luo Mingxing,et al.Remote preparation of afour-particle entangled cluster-type state[J].Optics Communications,2011,284(16):4088-4093.
Disclosure of Invention
The invention aims to provide a remote expansion method for realizing a cluster state based on a maximum entangled Bell state.
In order to solve the technical problem, the invention provides a remote expansion method for realizing cluster state based on maximum entanglement Bell state, which comprises the following steps:
constructing a distance extension path: the center node Alice enables the edge node Charlie to be assisted by the intermediate nodet(t ═ 1,2,3,4) enabling long range extension of cluster states; the central node Alice holds a set of partially entangled cluster states | C>1234(ii) a On the transmission path, the center node Alice and the edge node CharlietThe (t ═ 1,2,3 and 4) and the intermediate nodes are mutually connected in pairs, and share a maximum entanglement Bell state;
wherein Alice and Charlie1The intermediate node between them is marked asAlice has particles 1,2,3,4 and A1Intermediate nodeHaving particles A2iAnd particles A2i+1Edge node Charlie1Having particles A2p+2(ii) a Alice and other intermediate nodesAnd edge node Charliet(t ═ 2,3,4) particle assignments were similar;
channel modulation and measurement: center node Alice and edge node Charlie1Intermediate node betweenFor the own particle A2iAnd particles A2i+1Performing a Bell-based measurement; center node Alice and edge node Charlie3Intermediate node betweenFor own particles C2iAnd particles C2i+1Performing Bell-based measurement, and informing all measurement results through classical channel after completing Bell measurementA known center node Alice;
establishing a direct entanglement channel between the central node and the edge node: the central node Alice follows the intermediate nodeSelecting corresponding unitary operation to act on the particle A according to the sent measurement result1And edge node Charlie1Form a two-particle Bell entanglement channel, namely a particle A owned by a central node Alice1And edge node Charlie1Having particles A2p+2Collapsing into a pair of maximally entangled Bell states;
similarly, the particle C owned by Alice1And edge node Charlie3Having particles C2p+2Collapsing into a pair of maximally entangled Bell states;
completing the long-distance extension of cluster state: particle pair (1, A) in center node Alice opponent1),(3,C1) Bell-based measurements are performed, and Alice informs the edge nodes Charlie of the measurement results through classical channels respectively1And Charlie3(ii) a Edge node Charlie1And Charlie3According to the measurement result informed by Alice, the corresponding unitary transformation is carried out on the particles in the hands, so that the long-distance extension of the cluster state can be completed, namely the particles 2 and 4 in the Alice hands and the edge node Charlie1And Charlie3Particles A in the hand2p+2And C2p+2Entangle into cluster state;
the similar operations of the steps of 'channel modulation and measurement' and 'establishing a central node and an edge node direct entangled channel' are carried out, wherein the central node Alice and the edge node Charlie2And Charlie4Can realize the remote extension of the cluster state, and finally leads the edge node Charlie tot(t ═ 1,2,3,4) particles A in the hand2p+2,B2p+2,C2p+2,D2p+2Entangle into cluster state.
In the above technical solution, in the step of "constructing a distance extension path", a system composed of all quanta has the following form:
in the above technical solution, in the step "channel modulation and measurement", a system formed by all quanta has the following form:
wherein U is00=I,U01=Z,U10=X,U11=ZX。
In the above technical solution, in the step "establishing a direct channel entangled with a central node and an edge node", a system composed of all quanta has the following form:
wherein U is00=I,U01=Z,U10=X,U11=XZ。
The invention has the beneficial effects that:
1. the measurement results of the intermediate nodes can be transmitted simultaneously, so that the efficiency of information transmission is improved, and the requirement of constructing a complex quantum communication network can be met.
2. All the measurement modes adopted by the invention are Bell-based measurement and single-bit measurement, and the specific operation difficulty is greatly reduced.
3. The invention expands the communication distance, and enables the edge nodes not directly sharing the quantum entanglement pairs to realize quantum communication.
Drawings
FIG. 1 is a work flow diagram of the remote expansion method for implementing cluster state based on the maximum entangled Bell state.
FIG. 2 shows a center node Alice and an edge node Charlie in the method for realizing cluster state long-distance expansion based on the maximum entangled Bell state1The quantum entanglement channel simulation diagram.
FIG. 3 is a drawing of the present inventionCentral node Alice and edge node Charlie in remote extension method for realizing cluster state based on maximum entanglement Bell statetAnd (t is 2,3,4) quantum entanglement channel simulation diagram.
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. non-maximally entangled four-bit cluster state
The non-maximum entangled four-bit cluster state adopted by the invention is as follows:
|C>=a|0000>+b|0011>+c|1100>-d|1111>
wherein | a2|+|b2|+|c2|+|d2|=1
2. Bell base
The Bell basis is the maximum entanglement state formed by two particles, and forms a set of complete orthogonal bases of a four-dimensional Hilbert space, and the specific form is as follows:
3. pauli array
Some unitary matrices, also known as Pauli matrices, are also used in the present invention. The specific form is as follows:
the first embodiment is as follows: as shown in fig. 1, a method for implementing cluster state remote expansion based on a maximum entangled Bell state, taking an intermediate node as an example, includes:
step 1: and constructing a distance expansion path. The center node Alice enables the edge node Charlie to be assisted by the intermediate nodet(t ═ 1,2,3,4) enables remote extension of the cluster state. The central node Alice holds a set of partially entangled cluster states | C>1234. On the transmission path, the center node Alice and the edge node CharlietAnd (t ═ 1,2,3 and 4) and the intermediate nodes are mutually connected in pairs, and share a maximum entanglement Bell state with each other. The system of all quanta in this case has the following form:
wherein Alice and Charlie1The intermediate node between them is marked asAlice has particles 1,2,3,4 and A1Intermediate nodeHaving particles A2And particles A3Edge node Charlie1Having particles A4. Alice and other intermediate nodesAnd edge node CharlietThe particle distribution of (t ═ 2,3,4) was similar.
Step 2: and modulating and measuring a channel. Center node Alice and edge node Charlie1Intermediate node betweenFor the own particle A2And particles A3Performing a Bell-based measurement; center node Alice and edge node Charlie3Intermediate node betweenFor own particles C2And particles C3And executing the Bell base measurement, and informing all measurement results to the center node Alice through a classical channel after completing the Bell measurement. The system of all quanta in this case has the following form:
wherein U is00=I,U01=Z,U10=X,U11=ZX
And step 3: and establishing a direct entanglement channel between the central node and the edge node. The central node Alice follows the intermediate nodeSelecting corresponding unitary operation to act on the particle A according to the sent measurement result1And edge node Charlie1Form a two-particle Bell entanglement channel, namely a particle A owned by a central node Alice1And edge node Charlie1Having particles A4Collapse into a pair of maximally entangled Bell states.
Similarly, the particle C owned by Alice1And edge node Charlie3Having particles C4Collapse into a pair of maximally entangled Bell states.
TABLE 1 relationship comparison table for center node Alice to execute unitary transformation
The system of all quanta in this case has the following form:
wherein U is00=I,U01=Z,U10=X,U11=XZ
And 4, step 4: completing the long-distance extension of the cluster state. Particle pair (1, A) in center node Alice opponent1),(3,C1) Bell-based measurements are performed, and Alice informs the edge nodes Charlie of the measurement results through classical channels respectively1And Charlie3. Edge node Charlie1And Charlie3According to the measurement result informed by Alice, the corresponding unitary transformation is carried out on the particles in the hands, so that the long-distance extension of the cluster state can be completed, namely the particles 2 and 4 in the Alice hands and the edge node Charlie1And Charlie3Particles A in the hand4And C4Entangle into cluster state.
TABLE 2 relationship lookup table for edge nodes charlie performing unitary transformation
Performing similar operations as the steps (2) and (3), wherein the center node Alice and the edge node Charlie2And Charlie4Can realize the remote extension of the cluster state and finally obtain the edge node Charliet(t ═ 1,2,3,4) particles A in the hand4,B4,C4,D4Entangle into cluster state.
Example two: as shown in fig. 1, a remote expansion for implementing cluster state based on maximum entangled Bell state includes:
step 1: and constructing a distance expansion path. Central nodeAlice makes the edge node Charlie with the assistance of the intermediate nodet(t ═ 1,2,3,4) enables remote extension of the cluster state. The central node Alice holds a set of partially entangled cluster states | C>1234. On the transmission path, the center node Alice and the edge node CharlietAnd (t ═ 1,2,3 and 4) and the intermediate nodes are mutually connected in pairs, and share a maximum entanglement Bell state with each other. The system of all quanta in this case has the following form:
wherein Alice and Charlie1The intermediate node between them is marked asAlice has particles 1,2,3,4 and A1Intermediate nodeHaving particles A2iAnd particles A2i+1Edge node Charlie1Having particles A2p+2. Alice and other intermediate nodesAnd edge node CharlietThe particle distribution of (t ═ 2,3,4) was similar.
Step 2: and modulating and measuring a channel. Center node Alice and edge node Charlie1Intermediate node betweenFor the own particle A2iAnd particles A2i+1Performing a Bell-based measurement; center node Alice and edge node Charlie3Intermediate node betweenFor own particles C2iAnd particles C2i+1Performing Bell base measurement, and passing all measurement results through the classic after completing Bell measurementThe channel informs the central node Alice. The system of all quanta in this case has the following form:
wherein U is00=I,U01=Z,U10=X,U11=ZX
And step 3: and establishing a direct entanglement channel between the central node and the edge node. The central node Alice follows the intermediate nodeSelecting corresponding unitary operation to act on the particle A according to the sent measurement result1And edge node Charlie1Form a two-particle Bell entanglement channel, namely a particle A owned by a central node Alice1And edge node Charlie1Having particles A2p+2Collapse into a pair of maximally entangled Bell states.
Similarly, the particle C owned by Alice1And edge node Charlie3Having particles C2p+2Collapse into a pair of maximally entangled Bell states. The system of all quanta in this case has the following form:
wherein U is00=I,U01=Z,U10=X,U11=XZ
And 4, step 4: completing the long-distance extension of the cluster state. Particle pair (1, A) in center node Alice opponent1),(3,C1) Bell-based measurements are performed, and Alice informs the edge nodes Charlie of the measurement results through classical channels respectively1And Charlie3. Edge node Charlie1And Charlie3According to the measurement result informed by Alice, the corresponding unitary transformation is carried out on the particles in the hands, so that the long-distance extension of the cluster state can be completed, namely the particles 2 and 4 in the Alice hands and the edge node Charlie1And Charlie3In the handParticle A of2p+2And C2p+2Entangle into cluster state
Performing similar operations as the steps (2) and (3), wherein the center node Alice and the edge node Charlie2And Charlie4Can realize the remote extension of the cluster state and finally obtain the edge node Charliet(t ═ 1,2,3,4) particles A in the hand2p+2,B2p+2,C2p+2,D2p+2Entangle into 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 remote expansion method for realizing cluster state based on maximum entanglement Bell state is characterized by comprising the following steps:
constructing a distance extension path: the center node Alice enables the edge node Charlie to be assisted by the intermediate nodetWherein t is 1,2,3,4, realizing the remote extension of the cluster state; the central node Alice holds a set of partially entangled cluster states | C>1234(ii) a On a transmission path, the center node Alice and the middle node are mutually connected in pairs, and share a maximum entangled Bell state; at the same time, the edge node CharlietWherein t is 1,2,3,4, and the intermediate nodes are mutually connected in pairs, and share a maximum entanglement Bell state;
wherein Alice and Charlie1The intermediate node between them is marked asWherein i is 1,2, … p, Alice possesses particles 1,2,3,4 and a1Intermediate nodeWherein i is 1,2, … p, having particles A2iAnd particles A2i+1Edge ofNode Charlie1Having particles A2p+2;
Alice and Charlie2The intermediate node between them is marked asWherein i is 1,2, … p, Alice possesses particles 1,2,3,4 and B1Intermediate nodeWherein i is 1,2, … p, having particles B2iAnd particles B2i+1Edge node Charlie2Having particles B2p+2;
Alice and Charlie3The intermediate node between them is marked asWherein i is 1,2, … p, Alice possesses particles 1,2,3,4 and C1Intermediate nodeWherein i is 1,2, … p, having particles C2iAnd particles C2i+1Edge node Charlie3Having particles C2p+2;
Alice and Charlie4The intermediate node between them is marked asWherein i is 1,2, … p, Alice possesses particles 1,2,3,4 and D1Intermediate nodeWherein i is 1,2, … p, having particles D2iAnd particles D2i+1Edge node Charlie4Having particles D2p+2;
Channel modulation and measurement: center node Alice and edge node Charlie1Intermediate node betweenWherein i 1, 2.. p, for the own particle a2iAnd particles A2i+1Performing a Bell-based measurement; center node Alice and edge node Charlie3Intermediate node betweenWherein i is 1,2, … p, for the own particle C2iAnd particles C2i+1Executing Bell base measurement, and informing all measurement results to a central node Alice through a classical channel after completing the Bell measurement;
establishing a direct entanglement channel between the central node and the edge node: the central node Alice follows the intermediate nodeWhere i 1, 2.. p, the measurement results from which the corresponding unitary operation is selected to act on the particles a1And edge node Charlie1Form a two-particle Bell entanglement channel, namely a particle A owned by a central node Alice1And edge node Charlie1Having particles A2p+2Collapsing into a pair of maximally entangled Bell states;
meanwhile, the central node Alice is according to the intermediate nodeWhere i is 1,2, … p, the corresponding unitary operation is selected to act on the particle C1And edge node Charlie3Form a two-particle Bell entanglement channel between the two particles, so that the central node Alice has the particle C1And edge node Charlie3Having particles C2p+2Collapsing into a pair of maximally entangled Bell states;
completing the long-distance extension of cluster state: particle pair (1, A) in center node Alice opponent1),(3,C1) Bell-based measurements are performed, and Alice informs the edge nodes Charlie of the measurement results through classical channels respectively1And Charlie3(ii) a Edge node Charlie1And Charlie3According to the measurement result informed by Alice, the corresponding unitary transformation is carried out on the particles in the hands, so that the long-distance extension of the cluster state can be completed, namely the particles 2 and 4 in the Alice hands and the edge node Charlie1And Charlie3Particles A in the hand2p+2And C2p+2Entangle into cluster state;
the similar operations of the steps of 'channel modulation and measurement' and 'establishing a central node and an edge node direct entangled channel' are carried out, wherein the central node Alice and the edge node Charlie2And Charlie4Can realize the remote extension of the cluster state, and finally leads the edge node Charlie totWherein t is 1,2,3,4, particle A in hand2p+2,B2p+2,C2p+2,D2p+2Entangle into cluster state;
where p represents the number of intermediate nodes.
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