CN107612689A - A kind of quantum state teleportation method transmitted based on bypass flow in quantum network - Google Patents
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Abstract
The invention discloses a kind of quantum state teleportation method transmitted based on bypass flow in quantum network, Alice sends unknown multidimensional muliti-qubit Entangled State to Bob, including：Alice informs the qudit sums of the central server unknown multidimensional muliti-qubit Entangled State, central server selection transmitting path number and the via node number on the path by classical channel, makes qudit parallel and is balancedly transmitted by p paths；Under the assistance of each via node, central server is coordinated, and p bar quantum channels are set up between Alice and Bob；Alice coordinates unknown multidimensional muliti-qubit Entangled State by different quantum channels using quantum teleportation principle to send Bob to parallel；Bob performs unitary operations and recovers unknown multidimensional muliti-qubit Entangled State, completes transmit process.The present invention realizes parallel transmission of the unknown multidimensional muliti-qubit Entangled State in a plurality of transmitting path, and link has dynamic and flexibility, disclosure satisfy that the requirement for building complicated quantum communication network.
Description
Technical Field
The invention relates to a communication network and an information transmission method, in particular to a quantum state invisible transmission method, and especially relates to a construction method of an unknown multidimensional multi-quantum bit entangled state invisible transmission network based on shunt flow.
Background
Quantum information and quantum computing are emerging interdisciplinary disciplines established on the basis of quantum mechanical principles, classical information science and classical computing science. Due to the unique advantages of quantum communication such as large communication capacity and high safety, quantum communication technology has been rapidly developed in recent years, and branch protocols such as quantum secure direct communication, quantum conversation, quantum key distribution and the like are continuously updated and perfected.
In 1984, both Bennett and Brassard encoded binary information using four polarization states (0, 90, 45, and 135) of single photons, thereby proposing the first Quantum key distribution protocol (QKD), the BB84 protocol (see documents C.H. Bennett, G.Brassard Quantum cryptography: public key distribution and in: processing of the IEEE International Conference Computers, systems, and Signal Processing, 1984). In 2016, china emits the ink number of the first quantum communication satellite in the world, the preparation of entangled photons is completed by the satellite, and then the entangled photons are respectively sent to two ground observation stations (one is on Qinghai-Tibet plateau and the other is on Lijiang) which are far away from each other, and Bell tests show that the two photons are still in an entangled state. Therefore, the test breaks through all the records in the past, and the entanglement and distribution test of 1200 kilometers in magnitude is completed, which lays a foundation for constructing a global quantum communication network.
Researchers throughout the world have conducted extensive theoretical and experimental studies since Bennett et al proposed the quantum crypto-cryptosystem state in 1993 (see c.h. Bennett, g.bescard, et al. Telecommunications an unknown quantum state of state both metallic and ionic-podlsky-Rosen channels. Phys. Rev. Lett.,1993,70 (13)). Unlike super-dense coding, which uses shared entanglement and quantum channels to convey classical information, quantum invisible transport is the transport of quantum states using shared entanglement, local operations, and classical communication. In the quantum invisible transmission state, the state information of the quantum bit to be transmitted does not need to be known, but Alice must transmit classical information to Bob, and Bob can execute local operation to reproduce the unknown multi-dimensional multi-quantum bit entangled state. Information transmission and information processing processes between two communication parties can be completed by using a quantum invisible state transmission principle, and a repeater of a quantum communication network is constructed by the quantum invisible state transmission principle.
At present, two-energy-level quantum systems are most used in most of schemes related to quantum information and quantum computation, but multi-energy-level quantum systems are also gradually studied intensively. Simon et al propose a high-dimensional quantum state physical implementation scheme for quantum communication and information processing, which can design a high-capacity quantum communication and computation technique using an algorithmic encoding technique of the high-dimensional quantum state, and which can further improve the speed, efficiency, and network capacity of quantum information processing. Goyal et al also in 2014 a multi-dimensional quantum state stealth transport scheme based on linear optics.
The realization of long-distance quantum communication depends greatly on constructing a quantum network with high safety, high efficiency and high capacity. Many different implementations have been proposed for the construction of quantum networks and the problem of quantum information transfer in networks. In 2016, li, Z, et al proposed a multi-user quantum wireless communication network construction scheme based on multi-bit GHZ state, which constructs a two-layer network architecture protocol capable of ensuring information transmission speed and stability, and the scheme shows that the quantum network can greatly reduce the computational complexity and resource consumption. In 2017, xiong, PY, et al proposed a routing forwarding protocol scheme based on a partially entangled GHZ-state quantum wireless multi-hop backbone network, and quantum information can be invisibly transmitted between adjacent nodes by using the quantum invisible state principle. The scheme has the advantages that the routing process and the construction of the quantum channel are carried out simultaneously, and the information transmission method can reduce the total data packet and interface delay.
The research on the multi-bit quantum invisible transmission state also shows a great deal of excellent results, and 2015, zhang, b. et al propose a three-bit quantum state invisible transmission scheme based on a four-bit entangled state, which indicates that the four-bit entangled state can be utilized, and simultaneously an auxiliary bit and a c-Not operation are introduced to realize the invisible transmission of the three-bit quantum state. In 2012, zhou, p. et al proposed a multi-dimensional controllable arbitrary-dimension multi-quantum-state invisible transmission scheme based on a pure entangled quantum channel, which indicates that a non-maximum entangled state is used as a quantum channel, and the cooperation of multiple control parties can be used to realize the invisible transmission of a multi-bit quantum state of an arbitrary dimension, and that the probability of an unknown original state obtained by a receiver ensures that the scheme is optimal.
However, how to improve the information transmission efficiency and flexibility of quantum state invisible transmission still remains a problem to be solved in the field.
Disclosure of Invention
The invention aims to provide a quantum state invisible transmission method based on flow distribution transmission in a quantum network, which improves the information transmission efficiency and flexibility through dynamic selection of a transmission link.
In order to achieve the purpose of the invention, the technical scheme adopted by the invention is as follows: a quantum state invisible transmission method based on flow distribution transmission in quantum network is characterized in that a network terminal user Alice sends an unknown multidimensional multi-quantum bit entangled stateTo another end user Bob, comprising the steps of:
(1) The terminal user Alice informs the central server of the total number t of the qudit of the unknown multi-dimensional multi-quantum bit entangled state through a classical channel, the central server selects a proper transmission path number p, and then calculates the qudit number x transmitted by the ith path i And the number of relay nodes q on the path i Enabling t qudits to be transmitted through p paths in parallel and in a balanced mode; on the ith transmission path, x is shared between the end user Alice and the first relay node, between adjacent relay nodes, between the last relay node and the end user Bob i Taking the generalized Bell state as a quantum channel; wherein p is more than or equal to 1 and less than or equal to t, i =1,2, \ 8230;
(2) Each relay node passes through the owned qudit B t And A t+1 Performing a generalized Bell-state measurement, where t =1,2, \8230;, q i (ii) a i =1,2, \8230;, p, and informs the end user Bob of the measurement result through a classical channel, and Bob selects a corresponding unitary operation to establish a GBS state quantum channel with the end user Alice, namely the qudit A owned by the network end user Alice 1 And the qudit owned by another end user BobCollapsing into a pair of entangled high-dimensional qubits in a quantum state of GBS;
(3) Network terminal user Alice pairs qudit y and qudit A 1 Performing generalized Bell-state measurements, y =1,2, \ 8230;, t, and transmitting the measurement results to an end user Bob over a classical channel, bob performing a corresponding unitary operation at quditRestoring the initial state of the qudit y;
(4) When p paths complete the transmission task, t qudit states are all transferred to the qudit owned by the end user BobAt this time, the unknown multi-dimensional multi-quantum bit entangled stateInvisibility is transferred to by t quditThe quantum system is formed.
In the step (1), the unknown multidimensional multi-quantum bit entangled stateFor t bits d level quantum states, expressed as:
wherein, the first and the second end of the pipe are connected with each other,
x∈{00…0，00…1，…，d-1d-1…d-1}。
in the above technical solution, the method for the central server to select p transmission paths according to the total number t of the qudit of the unknown multi-dimensional multi-quantum bit entangled state includes: the central server enables the number of the qudits transmitted by p paths to meet the balance requirement according to a balance flow distribution algorithm, and the selected p paths respectively comprise q i After the path selection of each relay node is successful, the ith path transmits x i The number of the qudits is one,
the generalized Bell state is in the form of
The generalized Bell state measuring base used in the generalized Bell state measuring in the step (2) has the following form:wherein m, n =0,1,2, \ 8230, d-1, d is the number of energy levels of the quantum entanglement state,represents modulo d plus;
the end user Bob sends the measurement result according to each relay nodem t ,n t =0,1,2, \ 8230;, d-1, the corresponding unitary transformation is chosen in the form:
completing q at end user Bob i After the sub-unitary operation, the network end user Alice owns the qudit A 1 And qudit owned by another end user BobCollapsing into a pair of entangled high-dimensional qubits in a quantum state of the GBS state of the form:
all the qudit systems now have the following form:
in step (3), the end user Alice pairs qudit y and qudit A 1 A generalized Bell state measurement is performed, of the form:
wherein y =1,2, \ 8230;, t,
alice will measure the resultTransmitted to another end user Bob, bob to qudit through classical channelPerforming a corresponding unitary operation U mn To be at quditThe initial state of qudit y is restored.
The quantum state invisible transmission method based on the flow distribution transmission in the quantum network is suitable for the technical field of quantum communication networks and information transmission.
Due to the application of the technical scheme, compared with the prior art, the invention has the following advantages:
1. the invention adopts the shunt flow, the unknown multi-dimensional multi-quantum bit entangled state to be transmitted is not transmitted through a quantum channel any more, but t quantum states are transmitted respectively through p paths in a balanced manner, and the transmitted entangled state can be any multi-bit and any multi-energy-level quantum system, so that the transmission link selection has dynamic property and flexibility, the requirement of constructing a complex quantum communication network can be met, and the information transmission efficiency is improved.
2. According to the quantum state invisible transmission method, as the GBS state quantum channel is finally established between the network terminal user Alice and the other terminal user Bob, GBSM measurement, classical communication and local operation required by the whole process can be realized, and the efficiency of successful unknown state transmission is very high.
3. When a plurality of groups of sending parties and receiving parties exist, the method can utilize the existing link to carry out state transmission without additionally constructing a network; the method for sharing the link can reduce the complexity of the network, save resources and is easy to maintain.
Drawings
Fig. 1 is a flowchart of a quantum state invisible transmission method based on split-flow traffic transmission in a quantum network according to an embodiment of the present invention;
fig. 2 is a schematic diagram illustrating distribution of p transmission paths formed by a network end user Alice, another end user Bob, and relay nodes in the embodiment;
fig. 3 is a schematic transmission diagram illustrating that in the embodiment, after a GBS channel is established between a network end user Alice and another end user Bob, the end user Alice invisibly transmits a certain qudit y in an unknown multi-dimensional multi-quantum-bit entangled state;
FIG. 4 is a schematic diagram of a 2-bit unknown 2-dimensional 2-qubit entangled-state transport network according to a second embodiment;
FIG. 5 is a schematic diagram of two network end users Alice1 and Alice2 sharing a link for dynamic transmission.
Detailed Description
The invention is further described with reference to the following figures and examples:
the first embodiment is as follows: the main realization idea of the invention is as follows: in a long-distance communication system based on a quantum repeater, a network terminal user Alice sends an unknown multi-dimensional multi-quantum bit entangled state to another terminal user Bob through a plurality of transmission pathsWith the help of each relay node, a long-distance quantum channel between the terminal user Alice and the other terminal user Bob is established by utilizing an entanglement exchange principle, and then the quantum information transmission with safety and high efficiency is realized by combining a quantum invisible transmission state. The selection of the transmission path reflects the idea of shunting traffic, t qudits are divided into p groups and transmitted through p paths in parallel, and therefore the efficiency and the safety of quantum information transmission can be improved.
Referring to fig. 1 and fig. 2, a quantum state invisible transmission method based on split flow transmission in a quantum network includes the following steps:
step 1, network terminal user Alice wants to send unknown multi-dimensional multi-quantum bit entangled stateFor another end user Bob, firstly, the end user Alice informs the central server of the total number t of the qubits in the unknown multi-dimensional multi-quantum bit entangled state through a classical channel, the central server selects a proper transmission path number p (p is more than or equal to 1 and less than or equal to t), and then calculates the qubit number x transmitted by the ith (i =1,2, \ 8230;, p) path i (i =1,2, \8230;, p) and the number of relay nodes q on the path i (i =1,2, \8230;, p), thereby achieving simultaneous parallel and equalized transmission of t qudits over p paths. On each transmission path, x is shared between the end user Alice and the first relay node, between adjacent relay nodes and between the last relay node and the end user Bob i (i =1,2, \8230;, p) as quantum channels for the generalized Bell-state (GBS).
Wherein the unknown multi-dimensional multi-quantum bit entangled stateFor a t-bit d-level quantum state, then it must be written as follows:
wherein
x∈{00…0，00…1，…，d-1d-1…d-1}。
The process that the central server selects p (p is more than or equal to 1 and less than or equal to t) transmission paths according to the total number t of the qudit of the unknown multi-dimensional multi-quantum bit entangled state is as follows: the central server makes the transmitted qudit number of p paths balanced as much as possible according to a balanced distribution algorithm, and the selected p paths respectively comprise q i (i =1,2, \8230;, p) relay nodes, after the path selection is successful, the ith (i =1,2, \8230;, p) path is to transmit x i (i =1,2, \ 8230;, p) qudit, wherein
The above-mentionedThe Generalized Bell State (GBS) is in the form ofX is to be transported due to the i (i =1,2, \ 8230;, p) th path i (i =1,2, \8230;, p) qudit, so it is required that x is shared between the end user Alice and the first relay node, between the neighboring relay nodes, and between the last relay node and the end user Bob on the path i (i =1,2, \8230;, p) entanglement pairs as quantum channels.
Step 2, each relay node passes through the owned quditB t And A t+1 (t＝1,2,…,q i (ii) a i =1,2, \8230;, p) performs Generalized Bell State Measurement (GBSM) and informs the measurement result to the end user Bob through a classical channel, bob selects a corresponding unitary operation to establish a GBS state quantum channel with the end user Alice, namely, quditA owned by the end user Alice 1 And the qudit owned by another end user Bob(i =1,2, \8230;, p) collapses into a pair of entangled high-dimensional qubits in a quantum state that is a GBS state.
Wherein the Generalized Bell State Measurement (GBSM) uses a generalized bell state measurement base having the form:wherein m, n =0,1,2, \ 8230;, d-1,denoted modulo d plus.
The terminal user Bob sends the measurement result according to each relay node(t＝1,2,…,q i ；i＝1,2,…,p；m t ,n t =0,1,2, \8230;, d-1), the corresponding unitary transformation is chosen to have the following form:
completing q at end user Bob i (i =1,2, \8230;, p) qunit A owned by the end user Alice after a single operation 1 And qudit owned by another end user Bob(i =1,2, \8230;, p) collapses into a pair of entangled high-dimensional qubits in a quantum state of the GBS state of the following form:
in this case all the qudit composed systems have the following form:
step 3, as shown in fig. 3, the network end user Alice pairs qudit y (y =1,2, \8230;, t) and qudit a 1 Performing Generalized Bell State (GBSM) measurement and transmitting the measurement result to another end user Bob through a classical channel, and Bob performing corresponding unitary operation can perform at qudit(i =1,2, \8230;, p) the initial state of qudit y is restored.
Wherein the network end user Alice pairs qudity (y =1,2, \8230;, t) and qudit A 1 The GBSM measurement is performed in the form of:
wherein y =1,2, \ 8230;, t,
and measuring the resultTransmitted to another end user Bob, bob to qudit, via classical channelPerforming a corresponding unitary operation U mn Can be at qudit(i =1,2, \8230;, p) the initial state of qudit y is restored.
And 4, after the p paths complete the transmission task, transferring t qudit states to the qudit owned by the end user Bob(i =1,2, \8230;, p). At this time, unknown multidimensional multi-quantum bit entangled stateSuccessfully invisibly transfers t quditThe quantum system is formed.
Wherein, after p paths finish the transmission task, t qudit states forming the unknown state to be transmitted are all transferred to the qudit owned by the end user Bob(i =1,2, \8230;, p). In step 1, the P paths are determined by the central server according to a balanced distribution algorithm, the central server is responsible for reproducing an unknown multidimensional multi-quantum bit entangled state at a terminal user Bob, and the number of qudits transmitted by each path is x i (i =1,2, \8230;, p), wherein
The second embodiment:
in a 2-level 2-qubit quantum entangled state
Example of a transmission of where | a 0 | 2 +|a 1 | 2 +|a 2 | 2 +|a 3 | 2 ＝1。
Step 1, a network terminal user Alice initiates a service request to a central server, the central server selects a transmission path number p =2 according to a total number t =2 of qubits, and each path is supposed to contain a relay node number q i =1 (i =1,2). That is, the end user Alice transmits quantum states of qubit1 through path 1 (p = 1), and the relay node of the path is relay R1; quantum states of qubit2 are transferred over path 2 (p = 2), the relay node of which is relay R2;
as shown in fig. 4, on path 1, the end user Alice shares an entanglement pair with the relay node R1
Relay node R1 shares an entanglement pair with another end user BobWherein the end user Alice owns qubitA 11 The relay node R1 has a qbittB 11 And A 12 ，qubitB 12 Belonging to another end user Bob. The total system state on this path at this time is:
similarly, on path 2, the end user Alice shares an entanglement pair with the relay node R2
Relay node R2 and another terminalUser Bob shares entanglement pairsWherein the end user Alice has qubitA 21 The relay node R2 has a qubitB 21 And A 22 ，qubitB 22 Belonging to another end user Bob. The total system state on this path at this time is:
step 2, relay R1 to B 11 And A 12 Performing generalized bell state measurements (GBSM measurements) while relaying R2 to B 21 And A 22 A generalized bell state measurement (GBSM measurement) is performed, based on:
wherein m, n =0,1,modulo 2 plus is shown. Namely:
relay R1 measures qubit B using the above measurement basis 11 And A 12 So thatqubit A 11 And B 12 Collapse to with equal probability
R1 then measures the result over the classical channel Informing the end user Bob that Bob is based on the measurement resultSelecting corresponding unitary operation to construct GBS channel between end user Alice and another end user Bob, according toKnowing the unitary transformation:
U 00 ＝|0><0|+|1><1|
U 01 ＝|0><0|-|1><1|
U 10 ＝|0><1|+|1><0|
the relationship lookup table of the measurement results and the unitary transformation performed by the end user Bob is as follows:
TABLE 1
End user Bob to qubit B 12 The qubit A owned by the end user Alice after performing the unitary transformation 11 And qubit B owned by Bob 12 A GBS entangled state is formed,
similarly, relay R2 measures qubit B by similar operations as above 21 And A 22 And informing the end user of Bob measurement resultBob on qubit B 22 Corresponding unitary transformation U mn Enable a qubit A owned by an end user Alice 21 And a qubit B owned by another end user Bob 22 A GBS entangled state is formed,
step 3, constructing the quantum channel in the step 2, and collapsing the state of the whole combined system to:
network terminal user Alice pairs qubit1 and A 11 Performing GBSM measurements while on qubits 2 and A 21 Performing GBSM measurement and comparing the measurement resultAndinforming the other end-user Bob via the classical channel, bob individually responding to qu according to the following tablebit B 12 And B 22 And executing corresponding unitary operation:
TABLE 2
For example, when network end user Alice measures qubits 1 and A 11 Is in a system state ofqubits 2 and A 21 The system state ofThe end user Bob knows these two results over the classical channel, and then on the qubit B 12 And B 22 Perform the unitary operation separatelyAnd
step 4, when the transmission of the two paths is finished, the 2-energy-level 2-quantum bit is in an entangled state
Is successfully invisibly transferred to the user by qubit B 12 And B 22 On constructed quantum systems, i.e.
Wherein
|a 0 | 2 +|a 1 | 2 +|a 2 | 2 +|a 3 | 2 ＝1。
In this embodiment, a plurality of sending paths are established between two network terminal users to complete invisible transmission of unknown multidimensional multi-quantum bit entanglement states, and it should be noted that when there are a plurality of groups of sending parties and receiving parties, as shown in fig. 5, existing links can be used for carrying out state transmission without additionally establishing a network, and this method for sharing links can further reduce the complexity of the network, save resources, and is easy to maintain.
Claims (6)
1. A quantum state invisible transmission method based on flow distribution transmission in quantum network is characterized in that a network terminal user Alice sends an unknown multidimensional multi-quantum bit entangled stateTo another end user Bob, characterized in that it comprises the following steps:
(1) The terminal user Alice informs the central server of the total number t of the qudit of the unknown multi-dimensional multi-quantum bit entangled state through a classical channel, the central server selects a proper transmission path number p, and then calculates the qudit number x transmitted by the ith path i And the number of relay nodes q on the path i Enabling t qudits to be transmitted through p paths in parallel and in a balanced mode; on the ith transmission path, x is shared between the end user Alice and the first relay node, between adjacent relay nodes, between the last relay node and the end user Bob i Taking the generalized Bell state as a quantum channel; wherein p is more than or equal to 1 and less than or equal to t, i =1,2, \ 8230;
(2) Each relay node passes through the owned qudit B t And A t+1 A generalized Bell state measurement is performed, where t =1,2, \8230;, q i (ii) a i =1,2, \8230;, p, and informs the measurement result to the end user Bob through the classical channel, bob selects the corresponding unitary operation to establish the GBS state quantum channel with the end user Alice, namely the qudit A owned by the network end user Alice 1 And the qudit owned by another end user BobCollapsing into a pair of entangled high-dimensional qubits in a quantum state of GBS;
(3) For network terminalUser Alice pairs qudit y and qudit A 1 Performing generalized Bell-state measurements, y =1,2, \ 8230;, t, and transmitting the measurement results to an end user Bob over a classical channel, bob performing a corresponding unitary operation at quditRestoring the initial state of the qudit y;
(4) When p paths complete the transmission task, t qudit states are all transferred to the qudit owned by the end user BobAt this time, unknown multidimensional multi-quantum bit entangled stateInvisibility is transferred to t quditThe quantum system is formed.
2. The quantum state invisible transmission method based on split-flow traffic transmission in the quantum network of claim 1, characterized in that: in the step (1), the unknown multidimensional multi-quantum bit entangled stateFor t bits d level quantum states, expressed as:
wherein the content of the first and second substances,|{x}> 12…t-1 ，x∈{00…0，00…1，…，d-1d-1…d-1}。
3. the quantum state invisible transmission method based on the split flow transmission in the quantum network of claim 1, characterized in that: the method for selecting p transmission paths by the central server according to the total number t of the qudit of the unknown multi-dimensional multi-quantum bit entangled state comprises the following steps: the central server enables the transmitted qudit number of p paths to meet the balance requirement according to a balance flow distribution algorithm, and the selected p paths respectively comprise q i After the path selection of each relay node is successful, the ith path transmits x i The number of the qudits is,
4. the quantum state invisible transmission method based on split-flow traffic transmission in the quantum network of claim 1, characterized in that: the generalized Bell state is in the form of
5. The quantum state invisible transmission method based on the split flow transmission in the quantum network of claim 1, characterized in that: the generalized Bell state measuring base used in the generalized Bell state measuring in the step (2) has the following form:wherein m, n =0,1,2, \ 8230, d-1, d is the number of energy levels of the quantum entanglement state,represents modulo d plus;
the end user Bob sends the measurement result according to each relay nodem t ,n t =0,1,2, \8230;, d-1, the corresponding unitary transformation is chosen in the following form:
completing q at end user Bob i After the secondary unitary operation, the network end user Alice owns the qudit A 1 And qudit owned by another end user BobCollapsing into a pair of entangled high-dimensional qubits in a quantum state of the GBS state of the form:
in this case all the qudit composed systems have the following form:
6. the quantum state invisible transmission method based on the split flow transmission in the quantum network of claim 1, characterized in that: in step (3), the end user Alice pairs qudit y and qudit A 1 A generalized Bell state measurement is performed, of the form:
wherein y =1,2, \8230;, t,
alice will measure the resultTransmitted to another end user Bob, bob to qudit through classical channelPerforming a corresponding unitary operation U mn To at quditThe initial state of qudit y is restored.
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