CN106059680B - A kind of method of multi-hop transmission two-particle entangled state - Google Patents
A kind of method of multi-hop transmission two-particle entangled state Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
- H04B10/70—Photonic quantum communication
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
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Abstract
The invention discloses a kind of method of multi-hop transmission two-particle entangled state, Teleportation between two-particle entangled state two nodes apart from each other in quantum communication network is realized by being introduced into intermediate node, and by introducing auxiliary particle in destination node and to be transmitted two states successfully being recovered using unitary transformation.The method of multi-hop transmission two-particle entangled state in the present invention can not only provide the transmission of reliably and securely quantum information, in addition, state recovery is carried out by introducing auxiliary particle in destination node, improves the probability of two-particle entangled state transmission success between multiple nodes.
Description
Technical field
The invention belongs to quantum communications field, and in particular to a kind of method of multi-hop transmission two-particle entangled state, utilize two
Particle fraction Entangled State and maximum W states as quantum entanglement channel, realize two-particle entangled state two distant nodes it
Between multi-hop transmission.
Background technology
Quantum information is field of scientific study popular in recent years, generally includes quantum calculation and quantum communications.In quantum
In communication, quantum teleportation is a kind of most important and widely used method.Quantum communications are used as carrier by the use of quantum state
Information is transmitted, is a kind of brand-new communication mode, there is huge application prospect.In the last few years, researchers will research
Scope expands to the Teleportation of multiparticle from simple single-particle Teleportation, and expanding to part from maximal entangled state tangles
State.In quantum communication network, generally two kinds of channels, i.e. quantum channel and classical wireless channel be present.Quantum state is by tangling
Particle is to the transmission of quantum information in free space in a manner of Teleportation.Classical information in network, such as measurement result
Then transmitted by classical wireless channel.
Simultaneously as in quantum communication network, there is the problem of highly important quantum teleportation to need to solve,
I.e.：Source node can not be realized enjoys the resource tangled with other all purposes nodes in quantum communication network, in order to realize phase
Away from the Teleportation between two nodes farther out, multiple intermediate nodes are introduced, and each pair adjacent node is shared a pair and tangles source, with
This establishes source node to the quantum path between destination node.Therefore, the quantum multi-hop transmission side between multiple nodes is realized
Case has great importance.
The content of the invention
Goal of the invention：In order to solve problems of the prior art, the present invention proposes that a kind of particle of multi-hop transmission two entangles
The method for twining state, the transmission of reliably and securely quantum information can be not only provided, and two are improved by introducing auxiliary particle
The probability of Entangled transmission success between the multiple nodes of quantum communication network.
Technical scheme：To achieve these goals, in the present invention multi-hop transmission two-particle entangled state method, it is including following
Step：
(1) intermediate node is introduced between a source node and a destination node, and from source node to destination node, arbitrary neighborhood two saves
Point shares a pair of two particle fraction Entangled States and a pair of maximum W states, builds quantum entanglement channel；
(2) source node transmits two-particle entangled state along intermediate node until destination node successively.
Specifically, source node transmits two-particle entangled state along intermediate node until destination node, bag successively in step (2)
Include herein below：
Except destination node, to each node, to one of them particle state to be transmitted at the node and the grain of maximum W states
Son carries out Bell base measurements, and Bell base measurements are carried out to the particle of another particle state to be transmitted and two particle fraction Entangled States；
The particle of the maximum W states refers to the particle of the maximum W states of particle composition at the next node with the node, two particle unit
The particle of Entangled State is divided to refer to the particle of two particle fraction Entangled States of particle composition at the next node with the node；
At the next node of the node, the particle that selection forms maximum W states with particle at a upper node carries out shape
State measure, and according to state measurement judge upper hop particle state whether transmission success, if in the presence of successful probability, foundation
The Bell bases measurement result of upper hop chooses corresponding Pauli matrices and carries out state transformation to this node two particle waiting for transmission；Institute
It is another particle for being formed with particle at a upper node maximum W states to state one in this node two particle waiting for transmission, another
Individual is the particle for being formed with particle at a upper node two particle fraction Entangled States；
For destination node, the state of two particle waiting for transmission is then two particle entangleds at purpose node after state transformation
State.
More specifically, if particle state measurement result is | 1 ＞, in the absence of the probability of transmission success；If particle state is surveyed
Measuring result is | 0 ＞, then the probability of transmission success be present.
When two-particle entangled state is transferred to destination node, the not yet successful situation of two Particle Deliveries be present, therefore, the present invention
Method also further by introducing auxiliary particle at destination node, is recovered to the two-particle entangled state of not yet transmission success
Operation, it is specially：Appropriate unitary transformation U is selected according to the Bell bases measurement result of remaining each node in addition to destination node,
The two-particle entangled state transmitted at source node is recovered using the two-particle entangled state at destination node.
Further, if the state of auxiliary particle is | during 1 ＞, two particle entangleds transmitted at source node can not be recovered
State；If the state of auxiliary particle is | 0>When, then successfully recover the two-particle entangled state transmitted at source node.
Beneficial effect：The method of multi-hop transmission two-particle entangled state in the present invention, two are realized by introducing intermediate node
Teleportation between Entangled two nodes apart from each other in quantum communication network, can be provided reliably and securely
The transmission of quantum information；Further, wanted by introducing auxiliary particle in destination node and successfully being recovered using unitary transformation
Two states of transmission, improve the probability of two-particle entangled state transmission success between multiple nodes.
Brief description of the drawings
Fig. 1 is the multi-hop transmission illustraton of model of the present invention；
Fig. 2 is multi-hop transmission illustraton of model when nodes are 3；
Fig. 3 is multi-hop Quantum Teleportation line map when nodes are 3.
Embodiment
The present invention is further described with reference to case study on implementation.
Multi-hop transmission scheme in the present invention is established under the background of quantum cordless communication network.As shown in figure 1, source node
Two particle states 1,2 to be transmitted be present, it is necessary to transmit this to two-particle entangled state in Alice (node N=1) place | ψ12>=α | 00>12+β|
11〉12(||α2||+||β2| |=1) to distant destination node Bob (node N=M+1) place, M-1 middle node is introduced in scheme
Point (node N=2 to node N=M), then co-exist in M+1 node in transmission path.Per two neighboring a pair of two particles of nodes sharing
Partially entangled statesWherein 0<n<1, and a pair of maximum W states
As quantum entangled source, quantum entanglement channel is formed.
Specifically introduce the present invention program by taking 3 node multi-hop transmissions in Fig. 2, Fig. 3 as an example, in figure, Alice is source node,
Bob is purpose node, and Candy is introduced intermediate node, particle 1,2 waiting for transmission and maximum W be present at source node Alice
The particle 6 of the particle fraction Entangled State of particle 3 and two of state；Exist and particle 3 at source node Alice at intermediate node Candy
Form the particle 4,5 of maximum W states, and particle 6 forms the particle 7 of two particle fraction Entangled States, with particle 9 at destination node Bob,
10 form the particle 8 of maximum W states, and the particle 11 of two particle fraction Entangled States is formed with particle 12；Exist most at destination node Bob
The particle 9,10 of big W states, the particle 12 of two particle fraction Entangled States, and the auxiliary particle Aux introduced.Source node Alice is needed
Transmit a pair of two-particle entangled states | ψ12＞=α | 00 ＞12+β|11〉12To distant destination node Bob.With reference to Fig. 2, Fig. 3,
The method of multi-hop transmission two-particle entangled state in the present invention comprises the following steps：
(1) intermediate node is introduced between a source node and a destination node, and from source node to destination node, arbitrary neighborhood two saves
Point shares a pair of two particle fraction Entangled States and a pair of maximum W states, builds quantum entanglement channel.
Alice and Candy shares a pair of two particle fraction Entangled States and a pair of maximum W states, the state of two particle fraction Entangled States
For：The state of maximum W states is：
Candy and Bob shares a pair of two particle fraction Entangled States and a pair of maximum W states, the state of two particle fraction Entangled States are：The state of maximum W states is：
So as to establish the quantum entanglement channel of adjacent node.
(2) source node transmitted successively along intermediate node two-particle entangled state until destination node except destination node, it is right
Each node, Bell base measurements are carried out to one of them particle state to be transmitted at the node and the particle of maximum W states, to another
The particle of individual particle state to be transmitted and two particle fraction Entangled States carries out Bell base measurements；The particle of the maximum W states refers to
Form the particle of maximum W states with particle at the next node of the node, the particle of the two particle fractions Entangled State refer to
Particle forms the particle of two particle fraction Entangled States at the next node of the node；At the next node of the node, selection with
Particle forms the particle progress state measurement of maximum W states at a upper node, and judges upper hop according to state measurement
Particle state whether transmission success, if in the presence of successful probability, the Bell bases measurement result according to upper hop chooses corresponding bubble
Sharp matrix carries out state transformation to this node two particle waiting for transmission；One in described node two particle waiting for transmission be with
Particle forms another particle of maximum W states at a upper node, and another is to form two particle fractions with particle at a upper node
The particle of Entangled State；For destination node, the state of two particle waiting for transmission is then two at purpose node after state transformation
Sub- Entangled State.
21) to the particle state to be transmitted 1 at source node Alice and maximum W states particle 3, and another particle to be transmitted
One particle 6 of the particle fraction Entangled State of state 2 and two carries out Bell base measurements respectively.
For intermediate node Candy, with source node Alice at particle 3 formed optional one in two particles of maximum W states
Particle for state measurement judge upper hop particle state whether transmission success, the present embodiment selection particle 4, another particle is then
Particle to be transmitted, in the present embodiment as particle 5；The state of particle 4 is measured, and utilizes the condition adjudgement upper hop of particle 4
Whether the transmission of particle state succeeds, if the state of particle 4 is | and 1>4, the probability of two-particle entangled state transmission success is 0, and quantum passes
State fails；If the state of particle 4 is | 0>4, then in the presence of successful probability, now chosen according to Bell bases measurement result corresponding
Pauli matrices operate to two particles 5,7 waiting for transmission at next node Candy.
Assuming that m1,m3,m2,m6Represent Bell base measurement results, the formula of corresponding Pauli matrices is at each nodeWherein σx, σy, σzStandard Pauli matrices are represented,Represent to m3Value negate,
Represent to m1And m2Value take XOR.The then operation to particle 5 and 7 is： Representative pair
Particle 5 carries out σxOperation,Represent and σ is carried out to particle 7zOperation.Then, the state of tangling of particle 5,7 can be converted into α | and 00
>57+nβ|11>57Or n α | 00>57+β|11>57.Bell base measurement results correspond to m1,m3,m2,m6Expression it is as shown in table 1 below, its
In every time Bell base measurement results share 4 kinds of situations：|Φ+>、|Φ->、|Ψ->、|Ψ+>。
Table 1Bell base measurement results correspond to m1,m3,m2,m6Value
22) using step 21) identical mode to 5,8 and 7,11 points of particle at the next-hop node Candy of source node
Not carry out Bell base measurements, i.e., to particle state 5 to be transmitted and the particle 8 of maximum W states, and another particle state 7 to be transmitted with
The particle 11 of two particle fraction Entangled States carries out Bell base measurements respectively.It can determine whether the second jump passes state by measuring particle 9
Success, when the state of particle 9 is | 1>9, the probability of two-particle entangled state transmission success is 0, Teleportation failure；If the shape of particle 9
State is | 0>9, there is certain probability of success in two Particle Deliveries, according to the corresponding Pauli matrices of Bell bases measurement result selectionTwo particles 10 and 12 waiting for transmission at destination node Bob are operated, transmission success obtains
Particle state α | 00>1012+β|11>1012, now it is not required to carry out any particle manipulation again；Otherwise, the not yet successful shape of two Particle Deliveries
State then its be converted into α | 00>1012+n2β|11>1012Or n2α|00>1012+β|11>1012。
(3) when two-particle entangled state is transferred to destination node Bob, for the not yet successful state of two particles, due to now
Particle state be not particle state that source node initially transmits, by introducing auxiliary particle in destination node, and according to each node
Bell bases measurement result select appropriate unitary transformation U to recover the two-particle entangled state α initially transmitted | 00>+β|11
>。
Assuming that after carrying out i jump set state, it is α that the successful particle state of state is not yet passed at destination node | 00>+ni-2jβ|11>Or
ni-2jα|00>+β|11>, wherein j=0,1,2 ..., [(i-1)/2], what [(i-1)/2] represented (i-1)/2 in addition divides exactly portion
Point.
Postulated particle state is α | 00>+ni-2jβ|11>, then U form is as follows：
Postulated particle state is ni-2jα|00>+β|11>, then U form is as follows：
By taking the i=2 in the present embodiment as an example, that is, carry out passing for 2 times after state (as shown in Figure 2), at destination node Bob not yet
Successful state is then converted into α | and 00>1012+n2β|11>1012And n2α|00>1012+β|11>1012.Auxiliary particle Aux is introduced, to grain
10,12 and Aux of son carries out corresponding U operations, can recover the two-particle entangled state α initially transmitted | and 00>+β|11>, U shape
Formula is following (taking i=2, j=0 in corresponding formula (1), (2))：
Or
Now, can also be by measuring auxiliary particle Aux state, it can be determined that two-particle entangled state finally transmission whether into
Work(.When the state for measuring auxiliary particle Aux is | 1>AuxWhen, the final bust this of two-particle entangled state；When measuring auxiliary particle
Aux state is | 0>AuxWhen, show to have recovered the two-particle entangled state initially transmitted, two-particle entangled state finally transmits
Success.
Claims (5)
- A kind of 1. method of multi-hop transmission two-particle entangled state, it is characterised in that comprise the following steps：(1) intermediate node is introduced between a source node and a destination node, and from source node to destination node, the node of arbitrary neighborhood two is total to A pair of two particle fraction Entangled States and a pair of maximum W states are enjoyed, build quantum entanglement channel；(2) source node transmits two-particle entangled state along intermediate node until destination node successively.
- 2. the method for multi-hop transmission two-particle entangled state according to claim 1, it is characterised in that source is saved in step (2) Point transmits two-particle entangled state along intermediate node up to destination node, including herein below successively：Except destination node, to each node, one of them particle state to be transmitted at the node and the particle of maximum W states are entered Row Bell bases are measured, and Bell base measurements are carried out to the particle of another particle state to be transmitted and two particle fraction Entangled States；It is described The particle of maximum W states refers to the particle of the maximum W states of particle composition at the next node with the node, and two particle fraction entangles The particle for twining state refers to the particle of two particle fraction Entangled States of particle composition at the next node with the node；At the next node of the node, the particle that selection forms maximum W states with particle at a upper node carries out state survey Amount, and according to state measurement judge upper hop particle state whether transmission success, if in the presence of successful probability, according to upper one The Bell bases measurement result of jump chooses corresponding Pauli matrices and carries out state transformation to this node two particle waiting for transmission；Described One in node two particle waiting for transmission is another particle for being formed with particle at a upper node maximum W states, and another is The particle of two particle fraction Entangled States is formed with particle at a upper node；For destination node, the state of two particle waiting for transmission is then the two-particle entangled state at purpose node after state transformation.
- 3. the method for multi-hop transmission two-particle entangled state according to claim 2, it is characterised in that if particle state measures As a result it is | 1>, then in the absence of the probability of transmission success；If particle state measurement result is | 0>, then the general of transmission success be present Rate.
- 4. the method for multi-hop transmission two-particle entangled state as claimed in any of claims 1 to 3, it is characterised in that This method is further comprising the steps of：When two-particle entangled state is transferred to destination node, the not yet successful situation of two Particle Deliveries be present, introduced in destination node Auxiliary particle, and appropriate unitary transformation U, profit are selected according to the Bell bases measurement result of remaining each node in addition to destination node The two-particle entangled state transmitted at source node is recovered with the two-particle entangled state at destination node.
- 5. the method for multi-hop transmission two-particle entangled state according to claim 4, it is characterised in that if the shape of auxiliary particle State is | 1>When, then it can not recover the two-particle entangled state transmitted at source node；If the state of auxiliary particle is | 0>When, then succeed Recover the two-particle entangled state transmitted at source node.
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| CN109379183B (en) * | 2018-09-25 | 2021-03-23 | 苏州大学张家港工业技术研究院 | Multi-hop lossless invisible state transfer method based on non-maximum entangled chain channel |
| CN110350968B (en) * | 2019-07-16 | 2020-06-30 | 苏州大学 | D-dimensional chain type invisible state transferring method based on random sending of relay node measurement result |
| CN114422120B (en) * | 2021-12-21 | 2023-01-17 | 苏州大学 | High-dimensional multi-hop lossless invisible transmission method for channel modulation weight transfer |
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