CN114629562A - Quantum communication invisible state transfer optimization method based on non-maximum entangled state - Google Patents
Quantum communication invisible state transfer optimization method based on non-maximum entangled state Download PDFInfo
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Abstract
The invention discloses a quantum communication invisible state transfer optimization method based on a non-maximum entangled state, which relates to the technical field of quantum communication, and the method comprises the steps of firstly establishing a quantum communication combination system based on Alice and Bob; then, Alice and Bob respectively carry out combined Bell measurement on the particles owned by the Alice and the Bob and publish the measurement results; and finally, constructing the full appearance of the original quantum state transmitted by the other party by the Alice and the Bob by using the measurement result. The method takes (2n +2m) particles as channels, adopts a Bell state measurement mode to realize the asymmetric quantum invisible state, and completes the reconstruction of the initial particle states of the two parties with a certain probability. The invention adopts 4 particle states as channels to realize asymmetric quantum invisible transmission states, so that the channels of a communication protocol are more stable and are not easy to be interfered or damaged, the corresponding transmission efficiency is higher, and the physical realization is easy.
Description
Technical Field
The invention relates to the technical field of quantum communication, in particular to asymmetric bidirectional invisible state transfer and optimization based on a non-maximum entangled state.
Background
Quantum information is information represented by the state of microscopic particles. It is a discipline based on quantum mechanics, which studies how to perform computation, coding and information transmission in various ways through quantum systems. Quantum information is relative to classical information and is a novel discipline combining quantum mechanics and classical informatics. Quantum communication is an emerging cross-science combining quantum theory and communication theory. The method mainly relates to the research fields of quantum invisible state transfer, quantum super-dense coding, quantum state sharing, quantum information concentration and the like, wherein the quantum invisible state transfer is one of the most attractive subjects. The quantum invisible transport state is the most wonderful application in the field of quantum communication by utilizing quantum entanglement, and can realize instantaneous off-object transmission. The concept of quantum invisible state transport was proposed as early as 1993 by Bennett et al, a way to achieve remote state transport using classical channels and quantum entanglement resources. After this pioneering work, researchers have proposed many schemes for transferring unknown quantum states, such as unidirectional stealth, unidirectional controlled stealth, bidirectional stealth, etc., using different types of quantum channels. In 2002, Huelga et al first proposed a bidirectional quantum stealth mode, and many scholars have generated great interest in the research on the bidirectional quantum stealth mode and proposed a large number of schemes based on different quantum channels. Until 2013, Zha and the like propose a first quantum bidirectional controlled invisible transmission scheme by combining controlled and bidirectional invisible transmission ideas, wherein two information transmission parties can simultaneously exchange any single-particle unknown state of the two parties under the control of a third party. The quantum bidirectional controlled invisible state is taken as a new direction of the quantum invisible state, and great attention is paid to the quantum bidirectional controlled invisible state. Later some scholars proposed several schemes of bidirectional stealth states with different quantum entangled states as channels, but these schemes are symmetrical, for this case, in 2015, Zhang et al first proposed an asymmetric bidirectional controlled stealth scheme with 7-particle maximum entangled states as channels, under the control of a controller, Alice transmits her single particle state to Bob, and Bob can also transmit his two particle states to Alice. In 2019, Peng proposes an asymmetric bidirectional quantum information transmission scheme of a 9-quantum cluster state channel, and has the advantages that Alice adopts a special measurement basis, so that the number of selected channel particles is relatively less, and the transmission efficiency is improved. In the prior art, the channel stability of the existing protocol is poor, the existing protocol is easy to be interfered or damaged, and the transmission efficiency is low.
Disclosure of Invention
The present invention is directed to overcome the deficiencies of the prior art and provide a method for optimizing asymmetric quantum invisible states, so as to further stabilize the channel of the protocol without being easily interfered or damaged, and to improve the corresponding transmission efficiency.
The purpose of the invention is realized by the following technical scheme:
the quantum communication invisible state optimization method based on the non-maximum entangled state comprises the following steps:
the method comprises the following steps: establishing a quantum communication joint system based on Alice and Bob;
step two: alice and Bob respectively carry out combined Bell measurement on the particles owned by the Alice and the Bob and publish the measurement results;
step three: and constructing the full appearance of the original quantum state transmitted by the other party by using the measurement result by the Alice and the Bob.
Specifically, the first step specifically comprises: establishing a quantum communication joint system based on Alice and Bob, wherein Alice and Bob are a sender and a receiver of unknown arbitrary n particle states and m particle states, one non-maximum 2m +2n particle state is used as a quantum channel, and the state to be transmitted and the channel form the quantum communication joint system through tensor products.
Specifically, the second step is specifically as follows: in a quantum communication combined system, Alice and Bob form a particle pair by using the shared channel state and particles in an unknown arbitrary particle state to be sent, Bell measurement is performed on the particle pair under the Bell basis, and the respective Bell measurement results are published by Alice and Bob through a classical channel.
Specifically, the Alice and the Bob introduce auxiliary particles according to the measurement results of the Alice and the opposite Bell, construct unitary transformation, measure single particles of the auxiliary particles, separate collapse states of particle complexes formed by 2m +2n particle states after measurement into product states of two entangled-state particle quantum information shared by the Alice and the Bob, and reconstruct the original state of the opposite side at a certain probability through unitary transformation.
Specifically, in the first step, when n =2 and m =1, Alice and Bob respectively mutually obtain a sender and a receiver of any unknown 2-particle state and 1-particle state, one non-maximum 6-particle state is used as a quantum channel, and the state to be transmitted and the channel form a quantum communication joint system through tensor products.
Specifically, in the quantum communication combination system, a non-maximum 4-particle state is used as a quantum channel, and Alice and Bob respectively perform three-particle orthogonal basis measurement and single-particle projection measurement on corresponding particles and publish measurement results; in a quantum communication combined system, Alice and Bob form a particle pair by using the shared channel state and particles in an unknown arbitrary particle state to be sent, projection measurement is carried out on the particle pair under a three-particle orthogonal basis and a single particle respectively, and the measurement results of Alice and Bob are published through a classical channel;
alice and Bob introduce auxiliary particles according to the measurement results of the Alice and the other party, construct unitary transformation, measure the auxiliary particles with single particles, separate the collapse state of a particle complex consisting of 4 particle states after all measurements into a product state of two entangled-state particle quantum information shared by Alice and Bob, and reconstruct the original state of the other party with a certain probability through unitary transformation, wherein for the conditions of n =2 and m =1, the efficiency analysis comparison shows that the efficiency is higher by taking a non-maximum 4 particle state as a quantum channel.
The invention has the beneficial effects that:
1. according to the asymmetric quantum invisible state transfer and optimization method based on the non-maximum entangled state, the 2n +2m particle state is adopted as a quantum channel shared by Alice and Bob, so that asymmetric bidirectional transfer of quantum information is realized; because Alice and Bob are a sender and a receiver each other, Alice and Bob respectively carry out combined Bell measurement on the particles in the owned entangled state and the particles to be sent, and publish the measurement results through a classical channel, thereby realizing the simultaneous bidirectional transmission of quantum information, especially aiming at Alice and Bob respectively being a sender and a receiver which are unknown in any 2 particle states and 1 particle states, a non-maximum 6 particle states are generally required to be used as a quantum channel, the invention adopts a 4 particle state as the quantum channel, and has higher transmission efficiency than the prior art under the condition of transmitting the same information quantity through efficiency analysis and comparison; the collapse state of any unknown 2n +2m particle is restored to be the product state of original quantum information by combining the Bell measurement result of Alice and Bob, auxiliary particles are introduced to construct unitary transformation, single-particle measurement is carried out on the auxiliary particles, the collapse state of a particle complex formed by the 2m +2n particle states after measurement is separated into the product state of two entangled-state particle quantum information shared by Alice and Bob, and then the original state of the other party can be reconstructed at a certain probability by unitary transformation. When the channel is in the maximum entangled state, the success probability of the transfer and the restoration of the quantum information of the present embodiment is 1.
2. In order to explore the relationship between the 6 particle non-maximum entangled-state channel and the 4 particle non-maximum entangled-state channel, the invention analyzes and compares the corresponding efficiency to obtain the conclusion that the 4 particle non-maximum entangled-state channel scheme is more optimized.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a diagram of channel preparation for unknown arbitrary 2n +2m particle states of the present invention;
fig. 3 is a flow chart of an asymmetric bidirectional stealth state.
Detailed Description
The following detailed description will be selected to more clearly understand the technical features, objects and advantages of the present invention. It should be understood that the embodiments described are illustrative of some, but not all embodiments of the invention, and are not to be construed as limiting the scope of the invention. All other embodiments that can be obtained by a person skilled in the art based on the embodiments of the present invention without any inventive step are within the scope of the present invention.
The first embodiment is as follows:
in this embodiment, as shown in fig. 1, the quantum communication invisible state optimization method based on the non-maximum entangled state includes the following steps:
the method comprises the following steps: establishing a quantum communication joint system based on Alice and Bob;
step two: alice and Bob respectively carry out combined Bell measurement on the particles owned by the Alice and the Bob and publish the measurement results;
step three: and constructing the full appearance of the original quantum state transmitted by the other party by using the measurement result by the Alice and the Bob.
The optical quantum communication is mainly based on the theory of quantum entanglement state, and uses the quantum invisible state transfer (transmission) mode to realize information transfer. The process of optical quantum communication is as follows: a pair of particles with entangled states is constructed in advance, the two particles are respectively placed at two communication parties, the particles with unknown quantum states and the particles of a sending party are jointly measured (one operation), the particles of a receiving party are instantaneously collapsed (changed) into a certain state, the state is symmetrical to the state after the particles of the sending party are collapsed (changed), then the jointly measured information is transmitted to the receiving party through a classical channel, and the receiving party performs unitary transformation (equivalent to inverse transformation) on the collapsed particles according to the received information, so that the unknown quantum states which are completely the same as the sending party can be obtained.
Quantum invisible transport (Quantum termination), also known as Quantum remote transport or Quantum ionic transport, is the use of Quantum entanglement's indeterminate properties to transport the unknown Quantum state of a Quantum to another place (i.e., another Quantum in an EPR pair) through a Quantum of the EPR pair (entangled Quantum pair), while the original Quantum remains in place. Alice wants to communicate with Bob, and the specific flow is as follows:
(1) two entangled EPR quantum (particle) pairs were prepared and then separated, one for each of Alice and Bob, particle 1 and particle 2, respectively.
(2) Alice particle 1 and particle 3 of an unknown quantum state are jointly measured, and then the measurement result is transmitted to Bob through a classical channel.
The particle 2 held by Bob will change from a quantum state to a new quantum state as Alice measures the same time. This is due to the quantum entanglement effect, as if there is one or no one between particle 2 and particle 1.
(3) Bob makes a corresponding unitary transformation (a quantum computation transformation) based on the received information and the owning particle 2, from which information the full picture of the particle 3 can be reconstructed.
Compared with the traditional communication technology, the quantum communication has the following main characteristics and advantages:
(1) the timeliness is high. The time delay of a quantum communication line is nearly zero, the information efficiency of a quantum channel is dozens of times higher than that of a classical channel quantum, and the transmission speed is high.
(2) The anti-interference performance is strong. Information transmission in quantum communication does not pass through a traditional channel (for example, in order to prevent communication from being interfered in traditional mobile communication, frequency needs to be determined, and quantum communication does not need to consider the factors), is irrelevant to a propagation medium between two communication parties, is not influenced by a space environment, and has perfect anti-interference performance.
(3) The security performance is good. According to quantum unclonable theorem, quantum information can be irreducible change once detected, and if the quantum information is stolen in the middle of transmission, a receiver can discover the quantum information without fail.
(4) The concealment performance is good. Quantum communication has no electromagnetic radiation, and a third party cannot carry out wireless monitoring or detection.
(5) The application is wide. The quantum communication is independent of the transmission medium, the transmission cannot be blocked by any obstacle, and the quantum invisible transmission state communication can also pass through the atmosphere. Therefore, the quantum communication is widely applied, and can be used for communication in space, submarine communication and optical fiber and other media.
The implementation of the invention comprises the steps of establishing a quantum communication joint system based on Alice and Bob, preparing channel states, performing joint Bell measurement on the particles owned by Alice and Bob respectively, publishing measurement results, introducing secondary energy level particles, constructing the full appearance of the original particle state sub-state sent by the opposite side by Alice and Bob by using the measurement results, analyzing and comparing the efficiency of protocols under different channels, and the like, and specifically comprises the following steps:
suppose that Alice and Bob respectively have states to be transmitted as:
wherein the non-zero complex numbers a, b, c, d satisfy
。
They share one quantum channel of (2n +2m) particle state:
wherein
A non-zero complex number a1,a2,...,an+m，b1,b2,...,bn+mSatisfy the requirement of
,...,
Define | ai|<|bi|(i=1,2,⋯,n+m),|aj|<|aj+1L (| (j =1,2, ⋯, n + m-1). As shown in fig. 3, in order to realize the asymmetric bidirectional stealth state, the following steps are required:
step 1, channel preparation phase. To realize the asymmetric bidirectional invisible transmission state, a (2n +2m) particle entangled-state channel needs to be prepared locally. By aiming at the initial state |00 ⋯ 0 〉12⋯2n+2mHardmard's procedure was performed on particles with the sequence number 1,3, ⋯,2n +2m-1, and the particles were processedThe channel can be successfully prepared by performing a controlled not gate operation on (1,2), (3,4), ⋯, (2n +2m-1,2n +2 m). The specific operation flow is as follows:
hardmard's operation was performed on particles with serial numbers 1, 3.., 2n +2m-1, resulting in an initial state:
a controlled not gate operation is performed on the particle pair (1,2), (3,4), (2n +2m-1,2n +2m), where 1,3, ⋯,2n +2m-1 is the control bit, resulting in:
the local preparation was successful the preparation process is shown in figure 2.
And 2, a measuring stage. Particle x1,x2,⋯,xn1,3, ⋯,2n +2m-1 belongs to Alice, particle y1,y2,⋯,ym2,4, ⋯,2n +2m belongs to Bob, and the whole system state can be expressed as:
alice pairs of particles (x)1,1),(x2,3),⋯,(xn2n-1) carry out Bell measurements while Bob is on the particle pair (y)1,2n+2),(y2,2n+4),⋯,(ym2n +2m) are measured by Bell, the measurement results being 4 in totaln+mIn the method for preparing the seed coating,
wherein Bell radical is
。
And 3, a classical information transmission stage. Alice encodes her measurement results into classical information and sends the classical information to Bob through a classical channel; at the same time, Bob encodes his measurement results into classical information, which is sent to alice via a classical channel.
And 4, reconstructing a quantum state stage. Bob applies a corresponding unitary transformation to the particles 2,4, ⋯,2n, respectively, based on Alice's measurements. At the same time, Alice performs a corresponding unitary transformation on the particles 2n +1,2n +3, ⋯,2n +2m-1, respectively, according to Bob's measurements.
Note that deltaI=|0〉〈0|+|1〉〈1|；δz=|0〉〈0|-|1〉〈1|;
δx=|0〉〈1|+|1〉〈0|；iδy=|0〉〈1|-|1〉〈0|。
For example, Alice measures as
Bob has the measurement result of
The rest of the particles collapsed:
based on the received measurements, Bob needs to perform a unitary transformation on the particles (2,4, …,2n)
Meanwhile, Alice needs to perform unitary transformation on the particles (2n +1,2n +3, ⋯,2n +2m-1)
The following can be obtained:
to reconstruct the initial particle state, Bob and Alice should respectively introduce an initial state of |0 〉BAnd |0 〉AAnd (3) and (B) are respectively expressed at basis vector |00 〉 for formula (4)2B，|01〉2B，|10〉2B，|11〉2BAnd |00 〉(2n+1)A，|01〉(2n+1)A，|10〉(2n+1)A，|11〉(2n+1)AImplement the following unitary transformation U1And U2:
Equation (4) evolves to:
then, Bob and Alice respectively measure the respectively introduced auxiliary particles B and a using the computation basis |0 〉, |1 〉. If the measurements are all |0 〉, respectively, the transfer is successful, otherwise it fails. At this time, the probability of successful Alice transmission is
Bob has a probability of success of transmission of
。
For other measurement results of Alice and Bob, Bob and Alice only need to respectively carry out corresponding unitary transformation on the particles (2,4, ⋯,2n) and the particles (2n +1,2n +3, ⋯,2n +2m-1) according to the received measurement results and introduce the unitary transformationOne auxiliary particle makes one more single particle measurement, namely the particle state which Alice and Bob want to transmit can be respectively recovered through a certain probability
,...，
The success rate of both parties reaches 1.
When n =2 and m =1, Alice and Bob respectively have to-be-transmitted states as:
wherein the non-zero complex number a, b, c, d satisfies | a-2+|b|2=1，|c|2+|d|2They share one 6-particle non-maximally entangled state quantum channel, whose quantum channel is:
wherein the non-zero complex number c1，c2，c3，c4，a3，b3Satisfy | c1|=|a1a2|，|c2|=|a1b2|，|c3|=|a2b1|，|c4|=|a2b2|，|a1|2+|b1|2=1，|a2|2+|b2|2=1，|a3|2+|b3|2=1, stipulate | ai|<|bi|(i=1,2,3)，|aj|<|aj+1L (j =1,2), it is clear that the total probability of success of Alice delivery is 2| c1|2+2|c2|2Total probability of success of Bob transferIs 2| a3|2. If the corresponding channel is in the maximum entangled state, the probability of successful transmission in the asymmetric bidirectional transmission state is 1.
Considering that Alice and Bob transmit 2 particle states and single particle states to each other simultaneously respectively, a channel with less particles, such as 4 particle states, is adopted. Suppose that Alice and Bob respectively have states to be transmitted as:
wherein the non-zero complex number a, b, c, d satisfies | a2+|b|2=1，|c|2+|d|2=1。
They share a 4-particle quantum channel with non-maximum entanglement, which is:
wherein a non-zero complex number a1,b1,a2,b2Satisfy | a1|2+|b1|2=1,|a2|2+|b2|2=1, and specifies | a1|<|b1|，|a2|<|b2In order to realize the asymmetric bidirectional invisible state, the following steps are required:
step 1, measuring stage. Suppose particles 1,2, 4, 5 belong to Alice and particles 3, 6,7 belong to Bob. The overall system state can be expressed as:
the following 8 GHZ states constitute the three-particle orthogonal basis:
alice needs to perform Hadamard operations on particle 2 and then perform measurements on particle pairs (1,2,5) with three-particle orthogonal bases, while Bob performs single-particle projection measurements on particle 3, conceivably 16 measurements.
And 2, a classical information transmission stage. And the Alice encodes the measurement result into classical information and sends the classical information to Bob through a classical channel, and meanwhile, the Bob encodes the measurement result into classical information and sends the classical information to the Alice through the classical channel. The encoding rule is as follows:
and 3, reconstructing a quantum state stage. Bob performs a corresponding unitary transformation on the particles (6,7) according to the measurement result of Alice, and Alice performs a corresponding unitary transformation on the particles (4) according to the measurement result of Bob. The rules are as follows:
note that:
；
；
。
without loss of generality, assume Alice's measurement is λ+〉1,2,5Bob has a measurement of |0 〉3The remaining particles collapsed as:
from the received measurements Bob performs a unitary transformation on the particles (6,7)
While Alice performs a unitary transformation on the particles (4)
The following results were obtained:
to reconstruct the initial particle state, Bob and Alice need to introduce an initial state at |0 〉BAnd |0 〉AAnd (3) and a vector |00 〉 for formula (13) respectively6B，|01〉6B，|10〉6B，|11〉6BAnd |00 〉4A，|01〉4A，|10〉4A，|11〉4AImplement the following unitary transformation U3And U4:
The formula (13) evolves into
Then, Bob and Alice measure the respective introduced auxiliary particles B and a using the calculated basis |0 〉, |1 〉, respectively. If all the measurements are |0 〉, the transfer is successful, at which point Alice transfers toHas a power probability of
Bob has a probability of success of transmission of | a1|2(ii) a Otherwise, it fails.
Similarly, for other measurement results of Alice and Bob, Bob and Alice only need to respectively implement corresponding unitary transformation on the particles (6,7) and the particle (4) according to the received measurement results, introduce an auxiliary particle and then perform single particle measurement, and can respectively recover the particle states which are wanted to be transmitted by Alice and Bob, and the total probability of successful transmission is 2| a respectively2|2And 2| a1|2. In particular, when the channel is in the maximum entangled state, the two-party success rate reaches 1.
The method is discussed in terms of a general form of scheme for asymmetric bidirectional stealth modes. According to the general conclusion, when n =2 and m =1, the channel needs 6 particle states, and in fact, we find that the channel can be realized by adopting 4 particle states. To better explore the relationship between the construction schemes of the 6-particle channel and the 4-particle channel, we use the transmission efficiency as a tool to obtain table 1. The transmission efficiency is defined as
. Wherein p represents the number of constituent particles of the quantum information to be exchanged, q represents the number of particles of the channel, and t means the number of bits of classical resource consumption of transmission. From the channel point of view, it is easy to derive that the scheme with 4 particle states as channels is more optimized.
TABLE 1 transmission efficiency comparison Table
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (4)
1. The quantum communication invisible state optimization method based on the non-maximum entangled state is characterized by comprising the following steps of:
the method comprises the following steps: establishing a quantum communication joint system based on Alice and Bob;
the first step is specifically as follows: establishing a quantum communication joint system based on Alice and Bob, wherein Alice and Bob are a sender and a receiver of unknown arbitrary n particle states and m particle states, one non-maximum 2m +2n particle state is used as a quantum channel, and the state to be transmitted and the channel form the quantum communication joint system through tensor products;
step two: alice and Bob respectively carry out combined Bell measurement on the particles owned by the Alice and the Bob and publish the measurement results;
the second step is specifically as follows: in a quantum communication combined system, Alice and Bob form a particle pair by using a shared channel state and particles in an unknown arbitrary particle state to be sent, Bell measurement is carried out on the particle pair under the Bell basis, and the respective Bell measurement results are published by Alice and Bob through a classical channel;
step three: and constructing the full appearance of the original quantum state transmitted by the other party by using the measurement result by the Alice and the Bob.
2. The quantum communication invisible state optimization method based on the non-maximum entangled state according to claim 1, wherein Alice and Bob introduce auxiliary particles according to their own and opposite Bell measurement results to construct unitary transformation, perform single-particle measurement on the auxiliary particles, separate collapse states of all particle complexes consisting of 2m +2n particle states after measurement into product states of two entangled-state particle quantum information shared by Alice and Bob, and perform unitary transformation.
3. The quantum communication invisible state optimizing method based on the non-maximum entangled state according to claim 1, wherein in the first step, when n =2 and m =1, Alice and Bob respectively and mutually obtain a sender and a receiver of any unknown particle state 2 and particle state 1, one non-maximum particle state 6 is used as a quantum channel, and the state to be transmitted and the channel form a quantum communication combination system through tensor products.
4. The non-maximum entangled state based quantum communication invisible state optimization method according to claim 3, wherein a non-maximum 4 particle state is further used as a quantum channel in the quantum communication combination system, and Alice and Bob respectively perform three-particle orthogonal basis measurement and single-particle projection measurement on corresponding particles and publish measurement results; in a quantum communication combined system, Alice and Bob form a particle pair by using the shared channel state and particles in an unknown arbitrary particle state to be sent, projection measurement is carried out on the particle pair under a three-particle orthogonal basis and a single particle respectively, and the measurement results of Alice and Bob are published through a classical channel;
and introducing auxiliary particles by using the measurement results of Alice and Bob and the measurement results of the other party, constructing unitary transformation, carrying out single particle measurement on the auxiliary particles, separating the collapse state of a particle complex consisting of 4 particle states after all measurements into a product state of two entangled-state particle quantum information shared by Alice and Bob, and then carrying out unitary transformation.
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| CN115412177A (en) * | 2022-06-17 | 2022-11-29 | 中国人民解放军战略支援部队信息工程大学 | Cyclic controlled invisible state transfer method for any quantum state |
| CN115242316A (en) * | 2022-06-21 | 2022-10-25 | 苏州大学 | Lossless invisible state transfer method based on W-state channel |
| CN115242316B (en) * | 2022-06-21 | 2023-06-09 | 苏州大学 | Lossless invisible state transmission method based on W-state channel |
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