CN109218020B - Invisible transmission method based on unknown parameter four-bit cluster state - Google Patents
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- H—ELECTRICITY
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
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- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
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Abstract
The invention relates to an invisible transmission method based on an unknown parameter four-bit cluster state. The method mainly comprises five steps of (1) preparing a plurality of groups of same four-bit partially entangled cluster states by a channel preparation network center resource scheduling party, establishing a quantum partially entangled channel, and performing particle distribution on Alice and Bob. The method can realize the probability invisible transmission of the unknown two-particle state under the channel with unknown parameters, avoid the requirement on the maximum entangled channel and reduce the interference of quantum communication environment noise on quantum communication, greatly reduce the difficulty of specific communication control, and ensure that the invisible transmission of the unknown two-particle state is easier to physically realize.
Description
Technical Field
The invention relates to a communication network and an information transmission method, in particular to an invisible transmission method based on an unknown parameter four-bit cluster state.
Background
Quantum informatics is an interdisciplinary formed by quantum mechanics and information science. Quantum informatics provide new principles and methods for the continuous development and evolution of information science and communication technology. Currently, the main research directions of quantum informatics are quantum communication, quantum computing and quantum cryptography. The quantum communication mainly comprises three parts of quantum invisible transmission, quantum dense coding and quantum key distribution, and the quantum computation mainly comprises a quantum computer and a quantum computation method. Quantum informatics have received great attention from the birth date from many organizations and scholars at home and abroad. Especially in the aspect of quantum communication, scientists have focused their efforts on realizing quantum communication from theory since the last 90 s because of their characteristics such as high efficiency and absolute safety in information transmission.
The quantum invisible state is one of the most remarkable subjects in quantum information at present, is an important component of quantum information theory, and is also the basis of quantum computation. In 1993, six scientists in four countries such as Bennett united at phys.rev.lett published a paper [1] entitled "transporting unknown quantum states by classical and EPR channels", pioneering the research on quantum invisible transport (quantum telecommunications), and thus arousing the research interest on quantum invisible transport. After the publication of the pioneering papers by Bennett et al, extensive and intensive research into quantum invisible states has been carried out, and solutions for quantum invisible states have been presented in succession: in 1995, Brassard G et al proposed the use of a quantum loop consisting of a controlled NOT gate and a single qubit operation to implement a quantum invisible transport scheme [2 ]; in 1997, zheng shita proposed a cavity QED based quantum invisible transport scheme [3 ]; in 1998, Nielsen et al proposed a solution to achieve invisible propagation through non-maximally entangled states [4 ]; the 2000 and 2002 Guo Brilliant groups respectively provide a two-particle entangled state invisible state scheme [5] and a three-particle GHZ state invisible state scheme [6 ]; in 2005, Bae et al proposed a three-way quantum invisible state scheme [7] in any asymmetric state; since 2005, the rising billows group proposed wireless ad hoc quantum communication networks and studied the related protocols for such networks for wireless quantum communication networks of complex structure [8-10 ]. Quantum invisible transport is the transport of quantum states using shared entanglement, local manipulation 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.
The cluster state [11] is a new quantum entanglement state proposed by H J Briegel and R Raussendorf in 2001, and it is proved that the cluster state has some more specific properties when the number of quanta N >3, and the cluster state can be prepared by various methods such as using an optical system, a cavity QED system, an ion trap system, and the like [12-15 ]. The four-bit cluster state has the properties of GHZ (Greenberger-Horne-Zeilinger) state [16] and W state, and has proved to have stronger capability of resisting decoherence than GHZ state [17], resisting quantum bit loss [18], maximizing connectivity and continuous entanglement, and the four-bit cluster state can also be used as a powerful tool to perform non-local area test [19-20 ]. Besides the important role in unidirectional quantum computation, the four-bit cluster state has wide application in other fields, for example, the four-bit cluster state can also be used in quantum direct secure communication. In recent years, some scholars and researchers at home and abroad have also developed a series of researches on cluster state concentration and have proposed a series of solutions. Chuudhury and Dhara, Indian scientists, proposed a cluster state concentration protocol based on linear optics [21 ]. An effective three-step cluster state entanglement concentration scheme based on cross-Kerr media is provided by a quantum information expert Zhang Shou topic group of extensive university in China [22 ]. Xu tintingling et al proposed a two-step entanglement concentration scheme based on cross-Kerr nonlinearity [23 ].
The present invention is referred to the following references:
[1]Bennett C H,Brassard G,Crepeau C,Jozsa R,Peres A,Wootters W K.Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J].Phys.Rev.Lett.,1993,70(13):1895～1899.
[2]Brassard G,Mann A.Measurement of the bell operator and quantum teleportation[J].Phys.Rev.A,1995,51(3):1727～1731
[3]Zheng S B,Guo G C.Teleportation of atomic state through the Raman atom-cavity-filed interaction[J].Phys.Lett.A,1997,232(3):171～174
[4]Nielsen M A,Knill E,Laflamme R.Complete quantum teleportation by nuclear magnetic resonance[J].Nature,1998,396:52～55
[5]Hong L,Guo G C.Teleportation of a two-particle entangled state via entanglement swapping[J].Phys.Lett.A,2000,276(6):209～212
[6]Liu J M,Guo G C.Quantum teleportation of a three-particle entangled state[J].Chin.Phys.Lett.,2002,19(4):456～459
[7]Bae J,Jin J,Kim J,et al.Three-party quantum teleportation with asymmetric states[J].Chaos Solitons&Fractals,2005,24(4):1047～1052
[8] ad Hoc network MAC layer protocol [ J ] for improving energy efficiency, Chao, Gekko, Biguano, etc., 2006,29(2): 256-266
[9] Seasahi Tao, Xunao, Zhen, etc. wireless self-organizing quantum communication network routing protocol [ J ] based on quantum remote transport state, 2012,61(22): 50-57
[10] New Ad hoc network route establishment algorithm [ J ] for balancing flow and improving network energy efficiency, Ann. electronic and information Proc, 2005,27(12): 1988-1993
[11]Briegel H J，Raussendor F R.Persistent Entanglement in Arrays of Interacting Particles[J].Physical Review Letters，2001，86(5)：910—913.
[12]Borhani M,LossD.Cluster states from Heisenberg interactions[J].Physical Review A,2005,71:032308.
[13]Walther P,Resch K J,Rudolph T,Scheneck E,Weinfurter H,Vedral V,Aspelmeyer M,Zeilinger A.Experimental one-way quantum computing[J].Nature,2005,434:169-176.
[14]Browne D E,Rudolph T.Efficient linear optical quantum computation[J].Physical Review Letters,2005,95:010501.
[15]Zou X B,Mathis W.Schemes for generating the cluster states in microwave cavity QED[J].Physical Review A,2005,72:013809.
[16]Nie Y Y，LI Y H，Wang A S.Semi-quantum information splitting using GHZ-type states[J].Quantum Information Processing，2013，12(1)：437—448.
[17]Dür W,Briegel H J.Stability of macroscopic entanglement under decoherence[J].Physical Review Letters,2004,92(18):180403.
[18]Raussendorf R,Briegel H J.Persistent entanglement in arrays of n interacting particle[J].Physical Review Letters,2001,86:910-913.
[19]Walther P,Aspelmeyer M,Resch K J.Experiment violation of a cluster state bell inequality[J].Physical Review Letters,2005,95(2):020403
[20]Kiesel N,Schmid C,Weber U.Experiment analysis of a four-qubit photon cluster state[J].Physical Review Letters,2005,95(21):210502.
[21]Choudhury B S,Dhara A.An entanglement concentration protocol for cluster states[J].Quantum Information Processing,2013,12(7):2577-2585.
[22]Si B,Su S L,Sun L L.Efficient three-step entanglement concentration for an arbitrary four-photon cluster state[J].Chinese Physics B,2013,22(3):030305.
[23]Xu T T,Xiong W,Ye L.Concentrating arbitrary four-photon less-entanglement cluster state by only single photons[J].Modern Physics Letters B,2012,26(32):1250214.
Disclosure of Invention
In view of the above, it is necessary to provide a stealth transmission method based on an unknown parameter four-bit cluster state.
An invisible transmission method based on unknown parameter cluster state comprises the following steps:
step 1, channel preparation, wherein an end user Alice and an end user Bob are two communication parties, a particle a and a particle b carry unknown quantum states and are held by the end user Alice, and the unknown two-particle state form is
Network center resource scheduling party prepares multiple groups of same four-bit cluster state | C4>1234、|C4>1'2'3'4'、
|C4>＝a0|0000>+b0|0011>+c0|1100>-d0|1111>As a quantum entanglement channel, in which the parameter a0,b0,c0,d0Unknown, wherein the end user Alice owns particle 1 and particle 3, and the rest are owned by the end user Bob;
step 2, matching measurement, wherein the end user Alice executes Bell-based measurement on the particle pair (a,1) and the particle pair (b,3) and publishes a measurement result, and the quantum system has the following form:
the terminal user Bob can obtain different forms according to the measurement result of the terminal user Alice
Then Bob will obtain
With a set of unknown parameters, four-bit state of clustering | C4>1'2'3'4'Performing Bell-based measurements, from which different forms of measurements can be obtained
Specifically, the end user Bob obtains the measurement result according to Alice
There are 16 cases that when Bob ignores the local operation, it can be classified into 4 types according to the parameter form of the measurement result, and then Bob will ignore the local operation
With a set of unknown parameters, four-bit state of clustering | C4>1'2'3'4'Executing BellAfter the basis measurement, obtain
There are 256 possible types of measurement results, and when Bob ignores local operations such as I, Z, XZ, X, etc., the measurement results can be classified into 16 types according to the parameter types of the measurement results, which is as follows:
it can be seen from the above expression that
In the form of
At this time, the
With squares, for which invisible transmission of four-bit cluster states of unknown parameters would not be possible, needs to be culled.
The end user Bob prepares a matching channel according to the measurement result, and Bob utilizes the owned multi-group channelThe four-bit cluster state matching combination is known as the parameter, and Bell measurement is carried out to find the result matched with the previous measurement result
Channels of the same or equivalent combination; in the state of two groups of unknown parameters Cluster
The specific description is as follows: the end-user Bob pairs of particles (B)1,A2) And particle pair (D)1,C2) Performing Bell-based measurements and applying to the particle A1And particles C1Executing corresponding unitary operation to obtain four different forms
It can be seen from the above expression that
Is of the form | C1>At this time, the
With squares, for which it would not be possible to achieveThe stealth transmission of the four-bit cluster state of the parameter is known to be required to be removed; when in use
Is of the form | C2>At this time, the
Of the parameter form and
matching; when in use
Is of the form | C3>At this time, the
Of the parameter form and
matching; when in use
Is of the form | C4>At this time, the
Of the parameter form and
and (4) matching.
And 3, recovering unknown quantum states, and successfully preparing various forms of | C by the terminal user Bob after completing the matching measurement>(ii) a The end user Bob selects and
form matched | C>By performing the Bell measurement and performing the recovery operation, it is possible to achieve an invisible transfer of the unknown two-particle state.
To be provided with
Form (1) of
Is prepared by
Is of the form | C2>To illustrate, for example:
wherein the content of the first and second substances,
user Bob pairs of particles (2', A)1) And particle pair (4', C)1) Performing Bell measurement, based on different Bell measurement results, on the particles B2And particles D2Performing corresponding unitary operation to obtain two different forms
When in use
At this point, the transmitted unknown two-particle quantum state is successfully recovered with unknown channel parameters.
The invisible transmission method based on the unknown parameter four-bit cluster state can realize the invisible transmission of the unknown two-particle state under the channel of the unknown parameter, avoid the requirement on the maximum entangled channel and reduce the interference of the quantum communication environmental noise to the quantum communication; all the adopted measuring modes are Bell-based measurement, so that the difficulty of specific communication control is greatly reduced, and the invisible transmission of the unknown two-particle state is easier to physically realize.
Drawings
Fig. 1 is a flowchart of an invisible transmission method based on four-bit cluster state with unknown parameters according to an embodiment of the present disclosure.
Fig. 2 is a schematic diagram of particle distribution of end users Alice and Bob based on an unknown parameter four-bit cluster state stealth transmission method according to an embodiment of the present disclosure.
Fig. 3 is a schematic diagram illustrating a principle of an invisible transmission method based on four-bit cluster state with unknown parameters according to an embodiment of the present disclosure.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1 to 3:
1. four-bit unknown parameter cluster state
The four-bit partially entangled cluster state adopted by the invention is in the following form:
|C>＝a0|0000>+b0|0011>+c0|1100>-d0|1111>
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. controlling a phase gate
A control phase gate (CZ gate) having two input qubits, a control qubit and a target qubit. The function is as follows: when the control qubit is at |1> simultaneously with the target qubit, the phases of the two bulk states are inverted by π. The corresponding matrix form is:
4. pauli array
Some unitary matrices, also known as Pauli matrices, are also used in the present invention. The specific form is as follows:
as shown in fig. 1, an invisible transmission method based on unknown parameter four-bit cluster state realizes that an end user Alice transmits an unknown two-particle state to another end user Bob through an unknown parameter four-bit cluster state channel, and includes the following specific steps:
step 1, channel preparation, wherein an end user Alice and Bob are two communication parties, a particle a and a particle b carry unknown quantum states and are held by the Alice, the Alice transmits the unknown two particle states to the Bob through an unknown parameter channel, and the unknown two particle states are in the form of
Network center resource scheduling party prepares multiple groups of same four-bit unknown parameter cluster state | C4>1234、|C4>1'2'3'4'、
|C4>＝a0|0000>+b0|0011>+c0|1100>-d0|1111>As quantum entanglement channel, parameter a0,b0,c0,d0Unknown, wherein the end user Alice owns particle 1 and particle 3, and the rest are owned by the end user Bob;
step 2, matching measurement, wherein the end user Alice executes Bell-based measurement on the particle pair (a,1) and the particle pair (b,3) and publishes a measurement result, and the quantum system has the following form:
wherein
TABLE 1 relationship LUT for end user Bob to perform unitary transformation
The terminal user Bob can obtain different forms according to the measurement result of the terminal user Alice
Then Bob will obtain
With a set of unknown parameters, four-bit state of clustering | C4>1'2'3'4'Performing Bell-based measurements, from which different forms of measurements can be obtained
Specifically, the end user Bob obtains the measurement result according to Alice
There are 16 cases that when Bob ignores the local operation, it can be classified into 4 types according to the parameter form of the measurement result, and then Bob will ignore the local operation
With a set of unknown parameters, four-bit state of clustering | C4>1'2'3'4'After performing Bell-based measurements, obtaining
There are 256 possible types of measurement results, and when Bob ignores local operations such as I, Z, XZ, X, etc., the measurement results can be classified into 16 types according to the parameter types of the measurement results, which is as follows:
TABLE 2 measurement results of end user Bob
And measurement results
Comparison table
It can be seen from the above table that
In the form of
At this time, the
With squares, for which invisible transmission of four-bit cluster states of unknown parameters would not be possible, needs to be culled.
The terminal user Bob prepares a matched channel according to the measurement result, Bob performs Bell measurement by using a plurality of groups of unknown parameters of four-bit cluster state matching combination and finds out the result of the previous measurement
Channels of the same or equivalent combination; four-bit cluster state owned by Bob and two unknown parameters of the four-bit cluster state
The specific description is as follows:
wherein
Bob pairs of particles (B)1,A2) And particle pair (D)1,C2) Performing Bell-based measurements and applying to the particle A1And particles C1Executing corresponding unitary operation to obtain four different forms
Table 3: bell measurement result and
parameter form comparison table
It can be seen from the above table that
Is of the form | C1>At this time, the
The parameter form of (2) has a square, and the invisible transmission of the four-bit cluster state of the unknown parameter cannot be realized in the form of (2) and needs to be eliminated; when in use
Is of the form | C2>At this time, the
Of the parameter form and
matching; when in use
Is of the form | C3>At this time, the
Of the parameter form and
matching; when in use
Is of the form | C4>At this time, the
Of the parameter form and
and (4) matching.
And 3, recovering unknown quantum states, and successfully preparing various forms of | C by the terminal user Bob after completing the matching measurement>(ii) a The end user Bob selects and
form matched | C>By performing the Bell measurement and performing the recovery operation, it is possible to achieve an invisible transfer of the unknown two-particle state.
To be provided with
Form (1) of
Is prepared by
Is of the form | C2>To illustrate, for example:
wherein the content of the first and second substances,
user Bob pairs of particles (2', A)1) And particle pair (4', C)1) Performing Bell measurement, based on different Bell measurement results, on the particles B2And particles D2Performing corresponding unitary operation to obtain two different forms
Table 4: bell measurement result and
parameter form comparison table
When in use
At this point, the transmitted unknown two-particle quantum state is successfully recovered with unknown channel parameters.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (1)
1. An invisible transmission method based on unknown parameters of four-bit cluster state is characterized by comprising the following steps:
step 1, channel preparation, wherein an end user Alice and an end user Bob are two communication parties, a particle a and a particle b carry unknown quantum states and are held by the end user Alice, and the unknown two-particle quantum state form is
Network center resource scheduling party prepares multiple groups of same four-bit cluster state | C4>1234、|C4>1'2'3'4'、
|C4>＝a0|0000>+b0|0011>+c0|1100>-d0|1111>As a quantum entanglement channel, in which the parameter a0、b0、c0And d0Unknown, wherein the end user Alice owns particle 1 and particle 3, and the rest are owned by the end user Bob;
step 2, matching measurement, wherein the end user Alice executes Bell-based measurement on the particle pair (a,1) and the particle pair (b,3) and publishes a measurement result, and the quantum system has the following form:
wherein the content of the first and second substances,
the terminalThe end user Bob obtains different forms according to the measurement result of the end user Alice
Then Bob will obtain
With a set of unknown parameters, four-bit state of clustering | C4>1'2'3'4'Performing Bell-based measurements, obtaining different forms based on Bell measurements
Specifically, the end user Bob obtains the measurement result according to Alice
There are 16 cases in which, when Bob ignores the local operation, it is classified into 4 types according to the parametric form of the measurement result, and then Bob will classify
With a set of unknown parameters, four-bit state of clustering | C4>1'2'3'4'After performing Bell-based measurements, obtaining
There are 256 cases, and when Bob ignores I, Z, XZ and X local operations, a total of 16 classes are classified according to the parameter form of the measurement result, as follows:
from the above expression, when
In the form of
And
at this time, the
The parameter form of (2) has a square, and the invisible transmission of four-bit cluster state of unknown parameters cannot be realized in the form, so that the unknown parameters are eliminated; the terminal user Bob prepares a matched channel according to the measurement result, Bob performs Bell measurement by using a plurality of groups of unknown parameters of four-bit cluster state matching combination and finds out the result of the previous measurement
Channels of the same or equivalent combination; in which two sets of unknown parameters are four-bit cluster states
And
the specific description is as follows: the end-user Bob pairs of particles (B)1,A2) And particle pair (D)1,C2) Performing Bell-based measurements and applying to the particle A1And particles C1Executing corresponding unitary operation to obtain four different forms
From the above expression, when
Is of the form | C1>At this time, the
The parameter form of (2) has a square, and the invisible transmission of four-bit cluster state of unknown parameters cannot be realized in the form, so that the unknown parameters are eliminated; when in use
Is of the form | C2>At this time, the
Of the parameter form and
and
matching; when in use
Is of the form | C3>At this time, the
Of the parameter form and
and
matching; when in use
Is of the form | C4>At this time, the
Of the parameter form and
and
matching;
step 3, recovering the unknown quantum state, and completingAfter matching measurement, the end user Bob successfully prepares various forms of | C>(ii) a The end user Bob selects and
form matched | C>And performing Bell measurement and performing recovery operation to realize invisible transmission of unknown two-particle quantum states.
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