CN115412177A - Cyclic controlled invisible state transfer method for any quantum state - Google Patents
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Abstract
The invention relates to a cyclic controlled invisible state transfer method of any quantum state, belonging to quantum invisible communication methods. In the invention, each communication party shares the constructed optional quantum channel in advance, and simultaneously circularly and invisibly transmits any entangled states of unknown single particles, two particles and three particles based on the quantum channel; each communication party carries out Bell-based measurement on the own entangled particles and publishes respective measurement results through a public channel; if the control party agrees to continue communication, the control party performs { + >, | - > } base measurement on the own particles and publishes own measurement result through a public channel; and each communication party respectively carries out corresponding unitary transformation on the own particles according to the published measurement result, and recovers the information to be invisibly transmitted. Through the process, the controlled cycle quantum invisible propagation state with the probability of 1 in any unknown single particle state, two particle states and three particle states is realized in a real sense.
Description
Technical Field
The invention relates to a cyclic controlled invisible state transfer method of any quantum state, belonging to quantum invisible communication methods.
Background
Quantum entanglement is the core of quantum information theory. On the one hand, entanglement can produce non-local correlation, which cannot be explained by local theory and real-world theory; on the other hand, it can also be used as a quantum resource. One important application is quantum invisible transport, which can transfer unknown quantum states to remote locations without direct physical transport. In 1993, bennett et al proposed the first quantum invisible transport protocol. Then, people propose various invisible transmission schemes based on entangled states such as Bell state, GHZ state, W state and the like, the number of invisible transmitted particles is gradually increased from single particle state to double particle state, three particle state and some special N particle state; at the same time, some research for transmitting high-dimensional quantum states has been correspondingly advanced.
In 2013, a bidirectional controlled quantum invisible transport (BCQT) protocol was proposed for the first time. In the BCQT protocol, alice and Bob are both a sender and a receiver, and can transmit quantum states in a mutual invisible manner under the supervision of Charlie of a controller. Since then, the bidirectional quantum invisible state has received much attention, and a multi-particle bidirectional (controlled) invisible state method based on various entangled states has been proposed.
In 2017, chen et al first proposed a cyclic invisible transport protocol using a six-quantum-bit entangled state as a quantum channel. In 2018, mulberry proves that the seven-quantum-bit entangled state can be used for realizing a perfect cyclic controlled invisible state of three arbitrary single-quantum-bit states. In 2019, li et al proposed a scheme of performing controlled-cycle quantum stealth state transfer on any two particles by using a ten-quantum-bit entangled state. Shao and Long propose a cyclic control invisible state transfer scheme for realizing unknown single qubits by using a given true seven qubit entangled state as a quantum channel, and popularize the scheme to a scene in which a general true seven qubit entangled state is used as a channel. Shi et al invented a method for circularly controlling asymmetric quantum stealth states by using a three-dimensional super-entangled state as a quantum channel to realize any single quantum state. In 2020, vikram Verma proposes a three-party controlled quantum invisible state scheme taking a GHZ-like state as a quantum channel.
The quantum states transferred in the method are all quantum entangled states which are asymmetrically transferred and are specific or symmetrically transferred, and for any common quantum states in any form, how to carry out circular invisible transfer is not given at present.
Disclosure of Invention
The invention aims to provide a cyclic controlled invisible state transfer method for any quantum state, so as to solve the problem that the current cyclic invisible state transfer method for any form of quantum state is lacked.
The invention provides a cyclic controlled invisible state transfer method of any quantum state to solve the technical problems, which comprises the following steps:
1) The quantum channel is selected for each communication party in a sharing mode, the communication parties comprise three participating communication parties and a control party, and the quantum channel is formed by direct products of any 6G states in 16G states and entangled states of { + >, | - >);
2) Distributing entangled particles to each communication party according to the selected quantum channel, so that the entangled particles owned by each communication party can jointly form the selected quantum channel;
3) Each communication party carries out Bell-based measurement on the own entangled particles and publishes respective measurement results through a public channel; the control method carries out { + >, | - >) base measurement on the own particles and publishes own measurement results through a public channel;
4) And each communication party respectively carries out corresponding unitary transformation on the own particles according to the published measurement result, and recovers the information to be invisibly transmitted.
The invention provides an arrangement method for distributing entangled particles in quantum channels for all communication parties, so that the entangled particles owned by all communication parties can jointly form a selected quantum channel, and all participating communication parties transmit based on any quantum state of the entangled particles; each communication party carries out Bell-based measurement on the own entangled particles and publishes respective measurement results through a public channel; the control method carries out { + >, | - >) base measurement on the own particles and publishes own measurement results through a public channel; and each party of communication carries out corresponding unitary transformation on the own particles according to the published measurement result, and recovers the information to be invisibly transmitted. Through the process, the invention realizes the real controlled cycle quantum invisible state transfer method with the probability of 1 for any unknown single particle state, two particle states and three particle states.
Further, the participating communication parties comprise three parties, wherein the first communication party possesses one entangled particle A, and the second communication party possesses two entangled particles B 1 、B 2 The third party has three entangled particles C 1 、C 2 、C 3 (ii) a The first communication direction invisibly transmits any single particle quantum state to the third communication party, the second communication direction invisibly transmits any two particle quantum states to the first communication party, and the third communication direction invisibly transmits any three particle quantum states to the second communication party.
According to the method, the communication parties are arranged, the number of particles owned by each communication party is different, and according to the set transmission direction, each communication party transmits the quantum state according to the particles owned by the communication party, so that the controlled-cycle quantum invisible state transmission scheme with the probability of 1 in any unknown single particle state, two particle states and three particle states in a real sense is provided.
Furthermore, the invisible transmission of any single-particle quantum state to the third communication party from the first communication party is | k |> A ＝a 0 |0>+a 1 |1>The second communication direction invisibly transmits any two particle quantum states to the first communication party as
The third communication party invisibly transmits any three-particle quantum state to the second communication party as
Wherein each coefficient is a complex constant, and | a 0 | 2 +|a 1 | 2 ＝1，|b 0 | 2 +|b 1 | 2 +|b 2 | 2 +|b 3 | 2 ＝1，|c 0 | 2 +|c 1 | 2 +|c 2 | 2 +|c 3 | 2 +|c 4 | 2 +|c 5 | 2 +|c 6 | 2 +|c 7 | 2 ＝1。
The invention provides a corresponding quantum cycle invisible state scheme based on the constructed quantum channel.
Further, the Bell measurement base used is
Further, the unitary transformation includes H gate operation, CNOT operation, identity transformation I = |0><0|+|1><1| and Paulic operator σ x ＝|0><1|+|1><0|，iσ y ＝|0><1|-|1><0|，σ z ＝|0><0|-|1><1|。
Further, the 16G states in the quantum channel are:
wherein { | +>,|->Is in the state of
Further, when the control party does not agree to perform the circular invisible communication, the communication parties do not perform corresponding operations on the particles owned by the control party, and the communication is directly ended.
When the control party does not agree with the cyclic stealth communication, the cyclic stealth communication can be directly ended.
Further, quantum loop communication in different directions of the participating communication parties is achieved by adjusting the entanglement particles in the shared quantum channel selected by the communication parties.
Further, each of the participating communication parties measures the entangled particles owned by the participating communication parties in any order or simultaneously when performing Bell-based measurements.
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FIG. 1 is a flow chart of a method of cyclically controlled stealth propagation of arbitrary quantum states;
fig. 2 is a schematic diagram of invisible transmission of any single-particle quantum state by each communication party in the embodiment of the invention.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
The method comprises the steps of firstly constructing a quantum channel shared by all communication parties, wherein the quantum channel is formed by the direct product of any 6G states in 16G states and the entanglement states of { + >, | - >) states; distributing the entangled particles for each communication party, enabling each communication party to have different numbers of entangled particles, enabling the entangled particles owned by each communication party to jointly form a selected quantum channel, and enabling each participating communication party to transmit based on any quantum state of each entangled particle; each communication party carries out Bell-based measurement on the entangled particles owned by each communication party and publishes respective measurement results through a public channel; the control method measures the { + > | - >) basis of the own particles and publishes the measurement result of the control method through an open channel; and the communication parties respectively carry out corresponding unitary transformation on the own particles according to the published measurement results to recover the information to be invisibly transmitted. The implementation flow of the method is shown in fig. 1. The specific process is as follows:
it is assumed that the communication parties in this embodiment include three participating communication parties, namely Alice, bob and Charlie, and a controller David, and Alice, bob and Charlie are both senders and receivers of information.
1. And constructing a quantum channel shared by all communication parties, wherein the quantum channel is formed by direct products of any 6G states in 16G states and entangled states of { + >, | -) states.
For the present embodiment, each participating communication party shares in advance the direct product and { | +of 6 example G states selected from 16G states>,|->The entangled states of the states constitute the quantum channel | χ >, where i u U belongs to {1,2,3,4,5,6}, and satisfies 1 ≦ i u ≤16：
The 16G states in a quantum channel are:
the 6 example G states and { | + >, | - >) states selected in this example are:
2. and distributing the entangled particles to each communication party according to the selected quantum channel, so that the entangled particles owned by each communication party can jointly form the selected quantum channel.
The quantum channel shared by three parties Alice, bob, charlie and a fourth party control party David participating in circular communication in the invention is formed by direct product and { | +of any 6G states in 16G states>,|->The entangled state of the } state. The result of the entangled particles distributed to each communication party by this embodiment based on the quantum channel selected by this embodiment is shown in FIG. 2, in which the particles (A, 1,7, 8) are owned by Alice and the particle (B) 1 , B 2 4,5,6,11, 12) particles (C) of Bob's proprietor 1 ,C 2 , C 3 2,3,9, 10) are owned by Charlie and particle 13 is owned by David.
Under the control of a controller David, based on the entangled particle distribution result, the invisible transmission of any single-particle quantum state | κ from Alice to Charlie can be simultaneously realized in the embodiment> A ＝a 0 |0>+a 1 |1>Invisible transmission of any two particle quantum states from Bob to Alice
Stealth transmission of arbitrary three-particle quantum states from Charlie to Bob
In the above formulaAll the coefficients of (a) are complex constants and satisfy the normalization condition | a 0 | 2 +|a 1 | 2 ＝1，|b 0 | 2 +|b 1 | 2 +|b 2 | 2 +|b 3 | 2 ＝1，|c 0 | 2 +|c 1 | 2 +|c 2 | 2 +|c 3 | 2 +|c 4 | 2 +|c 5 | 2 +|c 6 | 2 +|c 7 | 2 ＝1。
Respectively carrying out Bell-based measurement on the owned entangled particles by Alice, bob and Charlie, and publishing the measurement results of the Alice, the Bob and the Charlie through public channels; the control method carries out { | + >, | - > } base measurement on the own particles and publishes own measurement results through a public channel.
Bell measurement base is
And the realization of the circular invisible transmission method in the invention is irrelevant to the measurement sequence of the communication parties Alice, bob and Charlie.
Performing Bell-based measurement on particles (A, 1) in an Alice opponent, and publishing the measurement result by using 2-bit classical information through a public channel; in this embodiment, if the measurement result of Alice is
The system state collapses to:
bob individually controlled particles (B) 1 5) and (B) 2 6) performing Bell base measurement, and publishing the measurement result by using 4-bit classical information through a public channel; in this embodiment, if Bob has a measurement result of
And
the system state collapses to:
charlie respectively for the particles (C) 1 ,2),(C 2 ,9),(C 3 10) performing Bell-based measurement and publishing the measurement result by using 6-bit classical information through a public channel; in this embodiment, if the Charlie measurement result is
And
the system state further collapses to:
if the control party David agrees to continue the cyclic invisible communication, the control party David makes a call to the particles owned by the control party David
And (4) measuring the base. David in this example performs { | +on mastered particle 13>,|->Measuring based on the base, and publishing the measuring result by using 1-bit classical information through an open channel; in this embodiment, if David's measurement result is | +> 13 Then the system state further collapses to:
and 4, performing corresponding unitary transformation on the particles in the hands of the communication parties according to the measurement results published by the communication parties by Alice, bob and Charlie, and recovering the information to be invisibly transmitted.
In this embodiment, if the measurement results are respectively
And | +> 13 Unitary transformation of owned particles 3,4, 7,8, 11, and 12 by Alice, bob, and Charlie, respectively
The circular invisible transmission state can be realized.
The unitary transformation usually includes H gate, CNOT operation, identity transformation I = |0><0|+|1><1| and Paulic operator σ x ＝|0><1|+|1><0|，iσ y ＝|0><1|-|1><0|，σ z ＝|0><0|-|1><1|。
Through the above process, under the control of the controller David, alice may transmit any single-qubit entangled state to Charlie, charlie may transmit any three-qubit entangled state to Bob, and Bob may transmit any two-qubit entangled state to Alice. The quantum circulation invisible transmission state is realized independent of the measurement sequence of each communication party, namely Alice, charlie and Bob can carry out measurement according to any sequence. For this embodiment, as shown in fig. 2, what is achieved is cyclic communication from Alice to Charlie, bob to Alice, and Charlie to Bob, and cyclic communication from Alice to Bob, bob to Charlie, and Charlie to Alice can also be achieved by adjusting entangled particles owned by Alice, charlie, and Bob.
The invention provides a controlled cycle quantum invisible state transfer scheme with the probability of 1 of any unknown single particle state, two particle states and three particle states in a real sense for the first time. Through calculation, the communication efficiency of the method is about 23.1%, the communication process relates to Bell measurement and local unitary operation, the success rate of three-party controlled quantum cycle communication is 1, eavesdropping attack during message transmission in the communication process can be effectively prevented, and the method has universality and practicability.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, it should be noted that, for those skilled in the art, many modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (9)
1. A cyclic controlled stealth state transfer method for any quantum state is characterized by comprising the following steps:
1) The method comprises the steps that selected quantum channels are shared by communication parties, wherein each communication party comprises three participating communication parties and a control party, and each quantum channel is formed by direct products of any 6G states in 16G states and entangled states of { | + >, | - > } states;
2) Distributing entangled particles to each communication party according to the selected quantum channel, so that the entangled particles owned by each communication party can jointly form the selected quantum channel;
3) Each communication party carries out Bell-based measurement on the entangled particles owned by each communication party and publishes respective measurement results through a public channel; the control method carries out { + >, | - >) base measurement on the own particles and publishes own measurement results through a public channel;
4) And each communication party performs corresponding unitary transformation on the own particles according to the published measurement result to recover the information to be invisibly transmitted.
2. The method of any quantum state cyclic controlled invisibility of transition of claim 1, wherein the participating parties include three parties, a first party having one entangled particle A and a second party having two entangled particles B 1 、B 2 The third communication party has three entangled particles C 1 、C 2 、C 3 (ii) a The first communication direction invisibly transmits any single particle quantum state to the third communication party, the second communication direction invisibly transmits any two particle quantum states to the first communication party, and the third communication direction invisibly transmits any three particle quantum to the second communication partyA sub-state.
3. The method according to claim 2, wherein the invisible transmission of the arbitrary single-particle quantum state from the first communication party to the third communication party is | κ |> A ＝a 0 |0>+a 1 |1>The second communication direction invisibly transmits any two particle quantum states to the first communication party
The third communication party transmits any three-particle quantum state to the second communication party in an invisible way
Wherein each coefficient is a complex constant, and | a 0 | 2 +|a 1 | 2 ＝1，|b 0 | 2 +|b 1 | 2 +|b 2 | 2 +|b 3 | 2 ＝1，|c 0 | 2 +|c 1 | 2 +|c 2 | 2 +|c 3 | 2 +|c 4 | 2 +|c 5 | 2 +|c 6 | 2 +|c 7 | 2 ＝1。
4. The method according to claim 3, wherein the Bell measurement basis is
5. A method as claimed in claim 3, wherein the unitary transformation comprises H-gate operation, CNOT operation, identity transformation I = |0><0|+|1><1| and Paulic operator σ x ＝|0><1|+|1><0|，iσ y ＝|0><1|-|1><0|，σ z ＝|0><0|-|1><1|。
6. The method of cyclic controlled stealth states of any quantum state of claim 1 or 3, wherein the 16G states in the quantum channel are:
wherein { | +>,|->In the state of
7. The cyclic controlled stealth method for any quantum state according to claim 1 or 3, wherein when the controller does not agree to the cyclic stealth communication, each communicating party does not perform corresponding operations on the own particles, and the communication is directly ended.
8. The method of any quantum state of claim 2, wherein quantum-cycle communication in different directions among the participating communication parties is achieved by adjusting the entanglement particles in the selected shared quantum channel allocated to each communication party.
9. A method of cyclic controlled cloaking states of any quantum state as claimed in claim 2 or 3 wherein each participating correspondent performs the Bell-based measurements of its own entangled particles in any order or simultaneously.
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