CN111355537B - Estimation method of multi-degree-of-freedom invisible transmission state transmission efficiency under quantum noise - Google Patents
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Abstract
The utility model discloses a method for estimating the transmission efficiency of a multi-degree-of-freedom invisible transmission state under quantum noise, which comprises the following specific steps of interfering noise into a communication process, describing noise generation operators of different types of noise, constructing a polarization space super entangled quantum invisible transmission state, constructing a quantum noise model, calculating the quantum fidelity under the noise, and measuring the quantum invisible transmission state efficiency by utilizing the average fidelity. The utility model utilizes the method of super operator summation to superimpose four common quantum noises on the quantum bit, establishes a noise model by considering the noise influence of three different photons in the quantum invisible transmission state process, and mainly considers the noise influence of polarization entanglement in the state of maximum entanglement of quanta on default space degree of freedom, redefines average fidelity and selects proper quantum state according to specific conditions to ensure that the quantum invisible transmission state reaches optimal efficiency.
Description
Technical Field
The utility model relates to the field of quantum invisible state transmission, in particular to a method for estimating the invisible state transmission efficiency of multiple degrees of freedom under quantum noise.
Background
After the first successful realization of the quantum invisible state based on entanglement by the australian scientist in 1997, the quantum invisible state is realized in a plurality of physical systems including cold atoms, ion traps, superconductors and the like, early researches on the quantum invisible state are all carried out in an ideal environment, entanglement resources are the largest entangled state in the quantum system, perfect quantum invisible state is completed for an input state, namely the input state is identical to the output state, and the fidelity reaches the maximum value of 1. However, in the actual quantum invisible state transmission process, the quantum system cannot be completely isolated from the external environment and can be influenced by a plurality of external factors, wherein the most important factors include atmospheric absorption and scattering, atmospheric turbulence, background radiation, quantum noise and the like, and the influence can destroy the coherence of the quantum, namely the quantum noise process. In general, quantum noise is a quantum characteristic from an optical field, the quantum noise cannot be completely eliminated, and a quantum channel of the quantum noise is usually degraded from a maximum entanglement channel to a non-maximum entanglement channel or even to a mixed state quantum channel after the quantum noise is subjected to quantum noise in an ideal quantum invisible transmission state in the quantum invisible transmission state process. After the physical system is coupled with the noise environment, the continuous increase of quantum decoherence can be accelerated. Meanwhile, quantum entanglement with strong dependency on coherence can also occur in the process of entanglement attenuation, even entanglement sudden death, entanglement resources are not necessarily in the maximum entanglement state, the quantum entanglement fidelity is greatly influenced, and the efficiency of invisible transmission state is influenced. Therefore, in the actual quantum communication process, attenuation and noise in the channel must be considered in order to realize communication using the invisible transmission state.
Currently, most experimental implementations can only transmit quantum states of a single degree of freedom, whereas real quantum physical systems naturally possess properties of multiple degrees of freedom, even one of the simplest elementary particles, such as single photons, whose properties include wavelength, momentum, spin and orbital angular momentum, etc. The research works are based on single degree of freedom and local noise environment, the entanglement evolution characteristic, the noise characteristic and the entanglement measure characteristic under the joint influence of the multiple degree of freedom characteristic and several quantum noises are ignored, a large amount of quantum information resources are needed in the actual quantum invisible transmission state process, the requirement of the remote quantum invisible transmission state cannot be met, and the channel capacity is reduced. The influence of quantum noise on the fidelity of the superentangled quantum invisible state transmission is studied, and two indexes of the accepted fidelity and average fidelity are adopted to evaluate the quantum invisible state transmission efficiency, so that ideas are provided for improving the transmission efficiency, and the existing research limitations are improved.
By solving the main equation of the quantum, the quantum jump operator is used as the quantum noise for constructing different local independence, the noise is analyzed to act on the change of the average fidelity and the safety efficiency of the quantum in the different processes of the Bell state measurement of the invisible transmission state of the quantum, the unitary transformation of the receiver, the quantum channel and the like, and the average fidelity is always higher than 1/2 when the single noise acts on the quantum channel. Although the method can calculate the fidelity under the noise, the method still has the defect that the influence of common quantum noise on the invisible state transmission fidelity is not considered, so that the calculation of the fidelity is not accurate enough.
The four kinds of noise, namely bit flip noise, phase flip noise, depolarization noise and amplitude damping noise, act on the quantum stealth state efficiency conditions of different particles of the quantum stealth state, noise is mainly used for generating operators through the noise, the operators act on density matrixes of different particles, finally superposition and summation are carried out, the actual probability of change of quantum bits after noise interference is fully considered, the average fidelity under the noise is redefined, and the influence of different noise on the quantum stealth state efficiency is analyzed. However, the method still has the defects that the method only researches the quantum invisible transmission state on single degree of freedom, is not expanded to single photon multiple degrees of freedom, and has certain limitation.
Disclosure of Invention
The utility model aims to provide an estimation method of the invisible state transmission efficiency of multiple degrees of freedom under quantum noise so as to solve the problems in the background technology.
In order to achieve the above purpose, the present utility model provides the following technical solutions: the estimation method of the invisible transmission state transmission efficiency with multiple degrees of freedom under the quantum noise comprises the following specific steps:
s1: interfering noise into the communication process;
s2: a noise generation operator describing different types of noise;
s3: constructing a polarization space super entanglement quantum invisible transmission state;
s4: constructing a quantum noise model;
s5: calculating quantum fidelity under noise;
s6: measuring quantum invisible state transmission efficiency by using average fidelity;
preferably, the specific implementation steps of S3 are as follows:
3a: for two-dimensional 4 bits in two degrees of freedom modes of polarization space, the superentangled quantum channel is as follows:
wherein subscripts 2 and 3 represent two superentangled photons, |pi> 23 I.e. the communication channel, the corresponding density matrix is ρ ch P and S represent the degree of freedom of polarization and the degree of freedom of space, respectively;
3b: the degree of freedom of polarization of photons is affected by noise, and four bells in the degree of freedom of polarization are as follows:
wherein ,|τ>P One of the four Bell states corresponding to the degree of freedom of polarization when
When four bells are in the maximum entanglement state;
3c: the spatial degrees of freedom are relatively affected by noise, with four bells in the maximum entanglement:
wherein ,|σ>S One of four bell states corresponding to spatial degrees of freedom;
3d: assume that the input quantum state corresponding to particle 1 is:
wherein γ represents a real number of a relative phase between α and β, satisfying:
the density matrix corresponding to the input state is ρ in ＝|ψ 1 ><ψ 1 |；
3e: by performing the super entangled bell states projection measurement on the particles 1 and 2, the sender can project the particles 3 onto 16 super entangled bell states, and then the receiver performs appropriate unitary transformation according to the measurement result of the sender, converting the particles 3 into information of the input state.
Preferably, the specific implementation steps of S1 are as follows:
1a: the density matrix when noise acts on the qubit k is constructed as follows:
wherein ,Ej A noise generating operator representing one type of quantum noise;
1b: constructing a plurality of channel models after noise action according to the following formula:
wherein ,
the subscripts 1,2,3 denote the input particle 1, the channel particle 2, or the channel particle 3, respectively.
Preferably, the specific implementation steps of S2 are as follows:
2a: the noise generation operator for bit flipping noise is as follows:
wherein P represents flip |H>→|V>,|V>→|H>Probability of (2);
2b: the noise generation operator of phase inversion noise is described as:
wherein, P represents the probability of P inverting the phase of the qubit |H > - |H >;
2c: the noise generation operator for depolarization noise is as follows:
wherein the qubit depolarizes with probability P, i.e., the original channel system is replaced by I/2, while the probability of 1-P remains unchanged;
2d: the noise generation operator for the amplitude damping noise is as follows:
where P represents the probability of photon loss, E 2 The function of the operator is to determine the vertical polarization state |V>To a horizontal polarization state |H>I.e. a process corresponding to the loss of one energy quantum in a physical system, E 1 The operator will maintain the horizontal polarization state |H>Unchanged, the vertical polarization state |V is weakened>Is a function of the magnitude of (a).
Preferably, the specific implementation steps of S4 are as follows:
4a: the particles 1 of the input are respectively subjected to different noises, i.e. p 1 Not equal to 0, superentangled channel particles 2 and 3 are not affected by noise, i.e. p 2 ＝p 3 =0, channel model is:
wherein ,Ei The density matrix of the composite system under the influence of noise, representing the noise generating operators of the four types of noise, is:
4b: particles 2 and 3 of the superentangled channel suffer from the same noise (p 2 ＝p 3 The particles 1 to be transferred are protected from noise (p 1 =0) channel model of noise interference at interference is:
wherein ,Fj ，G k Noise generation operators representing four types of noise acting on superentangled channel particles 2 and 3, respectively, the density matrix of the composite system under the influence of noise is:
4c: when the particle 3 is given to the receiving side, the particle 3 is subjected to noise interference (p 3 Not equal to 0), it is assumed that particles 1 and 2 in the sender's hand are now protected from noise (p 1 ＝p 2 =0), the channel model of noise interference at this time is:
wherein ,Gk The density matrix representing the noise generating operator acting on the particles 3, the composite system subject to noise is:
preferably, the specific implementation steps of S5 are as follows:
5a: the quantum fidelity under the influence of noise is calculated according to the following formula:
F i ＝Tr[ρ in ρ out ]＝ 1 <ψ|ρ out |ψ> 1
wherein ,ρin Density matrix and p representing input states respectively out Representing the density matrix of the output state after the receiver performs unitary operation according to the measurement result of the sender in the noise environment, |ψ> 1 For the initial input state, when the output state and the input state are completely the same, the communication process carries out 100% error-free transmission, and the fidelity is the maximum value of 1;
5b: the average fidelity is defined as follows:
wherein, represents Q i Representing the probability that a quantum state actually occurs, the input states available to the sender also satisfy a particular probability distribution.
Preferably, the specific implementation steps of S6 are as follows:
assume that the available input state of the sender is |ψ> 1 According to step 3d, α, β, γ satisfies the following condition:
probability P satisfies
The method can obtain the following steps: />
The efficiency of quantum invisible states is quantified according to the following formula:
the utility model has the technical effects and advantages that:
(1) The channel capacity of the quantum invisible transmission state is improved, because the quantum invisible transmission state scheme of the existing noise channel is used for completing simple quantum communication under a single degree of freedom, the transmission efficiency is low, the channel capacity can not meet the requirement of remote transmission, but in practice, photons have the characteristics of multiple degrees of freedom, the super entanglement carries larger information, the occupied resources are fewer, so that the channel capacity is effectively improved, the remote control is easy, and the measurement and the control do not influence and destroy the particle state under other degrees of freedom, thereby having practical significance in the quantum communication;
(2) The optimal quantum state transmission efficiency is ensured, and due to different quantum noise influence degrees on fidelity, the optimal quantum state can be selected or the proper quantum state conversion can be performed, so that the efficiency of the quantum invisible state transmission protocol is changed and improved, and the optimal efficiency is ensured.
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FIG. 1 is a flow chart of the steps for implementing the present utility model.
Detailed Description
The following description of the embodiments of the present utility model will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present utility model, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the utility model without making any inventive effort, are intended to be within the scope of the utility model.
The utility model provides an estimation method of the invisible state transmission efficiency of multiple degrees of freedom under the quantum noise as shown in figure 1, which comprises the following specific steps:
s1: interfering noise into the communication process;
1a: the density matrix when noise acts on the qubit k is constructed as follows:
wherein ,Ej A noise generating operator representing one type of quantum noise;
1b: constructing a plurality of channel models after noise action according to the following formula:
wherein ,
subscripts 1,2,3 denote input particle 1, channel particle 2, or channel particle 3, respectively;
s2: a noise generation operator describing different types of noise;
2a: the noise generation operator for bit flipping noise is as follows:
wherein P represents flip |H>→|V>,|V>→|H>Probability of (2);
2b: the noise generation operator of phase inversion noise is described as:
wherein, P represents the probability of P inverting the phase of the qubit |H > - |H >;
2c: the noise generation operator for depolarization noise is as follows:
wherein the qubit depolarizes with probability P, i.e., the original channel system is replaced by I/2, while the probability of 1-P remains unchanged;
2d: the noise generation operator for the amplitude damping noise is as follows:
where P represents the probability of photon loss, E 2 The function of the operator is to determine the vertical polarization state |V>To a horizontal polarization state |H>I.e. a process corresponding to the loss of one energy quantum in a physical system, E 1 The operator will maintain the horizontal polarization state |H>Unchanged, the vertical polarization state |V is weakened>Is a magnitude of (a);
s3: constructing a polarization space super entanglement quantum invisible transmission state;
3a: for two-dimensional 4 bits in polarization-space two-degree-of-freedom mode, the superentangled quantum channel is as follows:
wherein subscripts 2 and 3 represent two superentangled photons, |pi> 23 I.e. the communication channel, the corresponding density matrix is ρ ch P and S represent the degree of freedom of polarization and the degree of freedom of space, respectively;
3b: the degree of freedom of polarization of photons is affected by noise, and four bells in the degree of freedom of polarization are as follows:
wherein ,|τ>P One of the four Bell states corresponding to the degree of freedom of polarization when
When four bells are in the maximum entanglement state;
3c: the spatial degrees of freedom are relatively affected by noise, with four bells in the maximum entanglement:
wherein ,|σ>S One of four bell states corresponding to spatial degrees of freedom;
3d: assume that the input quantum state corresponding to particle 1 is:
wherein γ represents a real number of a relative phase between α and β, satisfying:
the density matrix corresponding to the input state is ρ in ＝|ψ 1 ><ψ 1 ｜；
3e: by performing the super entangled bell states projection measurement on the particles 1 and 2, the sender can project the particles 3 onto these 16 super entangled bell states, and then the receiver performs appropriate unitary transformation according to the measurement result of the sender, the particles 3 are converted into information of the input state;
s4: constructing a quantum noise model;
4a: the particles 1 of the input are respectively subjected to different noises, i.e. p 1 Not equal to 0, superentangled channel particles 2 and 3 are not affected by noise, i.e. p 2 ＝p 3 =0, channel model is:
wherein ,Ei The density matrix of the composite system under the influence of noise, representing the noise generating operators of the four types of noise, is:
4b: particles 2 and 3 of the superentangled channel suffer from the same noise (p 2 ＝p 3 The particles 1 to be transferred are protected from noise (p 1 =0) channel model of noise interference at interference is:
wherein ,Fj ，G k Noise generation operators representing four types of noise acting on superentangled channel particles 2 and 3, respectively, the density matrix of the composite system under the influence of noise is:
4c: when the particle 3 is given to the receiving side, the particle 3 is subjected to noise interference (p 3 Not equal to 0), it is assumed that particles 1 and 2 in the sender's hand are now protected from noise (p 1 ＝p 2 =0), the channel model of noise interference at this time is:
wherein ,Gk The density matrix representing the noise generating operator acting on the particles 3, the composite system subject to noise is:
s5: calculating quantum fidelity under noise;
5a: the quantum fidelity under the influence of noise is calculated according to the following formula:
F i ＝Tr[ρ in ρ out ]＝ 1 <ψ|ρ out |ψ> 1
wherein ,ρin Density matrix and p representing input states respectively out Representing the density matrix of the output state after the receiver performs unitary operation according to the measurement result of the sender in the noise environment, |ψ> 1 For the initial input state, when the output state and the input state are completely the same, the communication process carries out 100% error-free transmission, and the fidelity is the maximum value of 1;
5b: the average fidelity is defined as follows:
wherein, represents Q i Representing the quantum state ρ out The probability of actually occurring, the input state available to the sender also satisfies a specific probability distribution;
s6: measuring quantum invisible state transmission efficiency by using average fidelity;
assume that Alice has an available input state of |ψ> 1 According to (3 d), the following conditions are satisfied for α, β, γ, which are consistent with the uniform probability distribution P:
probability P satisfies
The method can obtain the following steps: />
The efficiency of quantum invisible states is quantified according to the following formula:
the method solves the problem of limitation of the existing method for estimating the fidelity under the noise, expands the quantum invisible transmission state based on single degree of freedom to the quantum invisible transmission state with single photon and multiple degrees of freedom being superentangled, estimates the average fidelity of the invisible transmission state under the influence of the quantum noise, judges the influence of different types of noise on the invisible transmission state efficiency, selects the proper entangled state to ensure the efficiency of the superentangled quantum invisible transmission state protocol, and the estimation method of the influence of different quantum noise on the transmission fidelity is realized, properly adjusts the quantum channel according to the estimation result, thereby being beneficial to completing the quantum invisible transmission state process with high fidelity and large channel capacity and having practical significance on the quantum communication process.
Finally, it should be noted that: the foregoing description is only illustrative of the preferred embodiments of the present utility model, and although the present utility model has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described, or equivalents may be substituted for elements thereof, and any modifications, equivalents, improvements or changes may be made without departing from the spirit and principles of the present utility model.
Although embodiments of the present utility model have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the utility model, the scope of which is defined in the appended claims and their equivalents.
Claims (6)
1. The estimation method of the invisible transmission state transmission efficiency with multiple degrees of freedom under the quantum noise is characterized by comprising the following specific steps:
s1: interfering noise into the communication process;
s2: a noise generation operator describing different types of noise;
s3: constructing a polarization space super entanglement quantum invisible transmission state;
s4: constructing a quantum noise model;
s5: calculating quantum fidelity under noise;
s6: measuring quantum invisible state transmission efficiency by using average fidelity;
the implementation steps of the S3 are as follows:
3a: for two-dimensional 4 bits in two degrees of freedom modes of polarization space, the superentangled quantum channel is as follows:
wherein subscripts 2 and 3 represent two superentangled photons, |pi> 23 I.e. the communication channel, the corresponding density matrix is ρ ch P and S represent the degree of freedom of polarization and the degree of freedom of space, respectively;
3b: the degree of freedom of polarization of photons is affected by noise, and four bells in the degree of freedom of polarization are as follows:
wherein ,|τ>P One of the four Bell states corresponding to the degree of freedom of polarization when
When four bells are in the maximum entanglement state;
3c: the spatial degrees of freedom are relatively affected by noise, with four bells in the maximum entanglement:
wherein ,|σ>S One of four bell states corresponding to spatial degrees of freedom;
3d: assume that the input quantum state corresponding to particle 1 is:
wherein γ represents a real number of a relative phase between α and β, satisfying:
the density matrix corresponding to the input state is ρ in ＝|ψ 1 ><ψ 1 |；
3e: by performing the super entangled bell states projection measurement on the particles 1 and 2, the sender can project the particles 3 onto 16 super entangled bell states, and then the receiver performs appropriate unitary transformation based on the measurement result of the sender, converting the particles 3 into information of the input state.
2. The method for estimating the transmission efficiency of the invisible transmission state with multiple degrees of freedom under the quantum noise according to claim 1, wherein the method is characterized by comprising the following steps of: the implementation steps of the S1 are as follows:
1a: the density matrix when noise acts on the qubit k is constructed as follows:
wherein ,Ej A noise generating operator representing one type of quantum noise;
1b: constructing a plurality of channel models after noise action according to the following formula:
wherein ,
the subscripts 1,2,3 denote the input particle 1, the channel particle 2, or the channel particle 3, respectively.
3. The method for estimating the transmission efficiency of the invisible transmission state with multiple degrees of freedom under the quantum noise according to claim 1, wherein the method is characterized by comprising the following steps of: the implementation steps of the S2 are as follows:
2a: the noise generation operator for bit flipping noise is as follows:
wherein P represents flip |H>→|V>,|V>→|H>Probability of (2);
2b: the noise generation operator of phase inversion noise is described as:
wherein, P represents the probability of P inverting the phase of the qubit |H > - |H >;
2c: the noise generation operator for depolarization noise is as follows:
wherein the qubit depolarizes with probability P, i.e., the original channel system is replaced by I/2, while the probability of 1-P remains unchanged;
2d: the noise generation operator for the amplitude damping noise is as follows:
where P represents the probability of photon loss, E 2 The function of the operator is to determine the vertical polarization state |V>To a horizontal polarization state |H>I.e. a process corresponding to the loss of one energy quantum in a physical system, E 1 The operator will maintain horizontal polarizationState |H>Unchanged, the vertical polarization state |V is weakened>Is a function of the magnitude of (a).
4. The method for estimating the transmission efficiency of the invisible transmission state with multiple degrees of freedom under the quantum noise according to claim 1, wherein the method is characterized by comprising the following steps of: the implementation steps of the S4 are as follows:
4a: the particles 1 of the input are respectively subjected to different noises, i.e. p 1 Not equal to 0, superentangled channel particles 2 and 3 are not affected by noise, i.e. p 2 ＝p 3 =0, channel model is:
wherein ,Ei The density matrix of the composite system under the influence of noise, representing the noise generating operators of the four types of noise, is:
4b: particles 2 and 3 of the superentangled channel suffer from the same noise (p 2 ＝p 3 =p), the input particles 1 are immune to noise (p 1 =0) channel model of noise interference at interference is:
wherein ,Fj ，G k Noise generation operators representing four types of noise acting on superentangled channel particles 2 and 3, respectively, the density matrix of the composite system under the influence of noise is:
4c: when the particle 3 is given to the receiving side, the particle 3 is subjected to noise interference (p 3 Not equal to 0), it is assumed that particles 1 and 2 in the sender's hand are now protected from noise (p 1 ＝p 2 =0), the channel model of noise interference at this time is:
wherein ,Gk The density matrix representing the noise generating operator acting on the particles 3, the composite system subject to noise is:
5. the method for estimating the transmission efficiency of the invisible transmission state with multiple degrees of freedom under the quantum noise according to claim 1, wherein the method is characterized by comprising the following steps of: the implementation steps of the S5 are as follows:
5a: the quantum fidelity under the influence of noise is calculated according to the following formula:
F i ＝Tr[ρ in ρ out ]＝ 1 <ψ|ρ out |ψ> 1
wherein ,ρin Density matrix and p representing input states respectively out The density matrix of the output state after the receiver receives the measurement result of the sender and performs unitary operation in the noise environment> 1 For the initial input state, when the output state and the input state are completely the same, the communication process carries out 100% error-free transmission, and the fidelity is the maximum value of 1;
5b: the average fidelity is defined as follows:
wherein, represents Q i Representing the quantum state ρ out The probability of actually occurring, the input state available to the sender also satisfies a particular probability distribution.
6. The method for estimating the transmission efficiency of the invisible transmission state with multiple degrees of freedom under the quantum noise according to claim 1, wherein the method is characterized by comprising the following steps of: the implementation steps of the S6 are as follows:
assume that the available input state of the sender is |ψ> 1 According to step 3d, α, β, γ satisfies the following condition:
probability P satisfies
The method can obtain the following steps: />
The efficiency of quantum invisible states is quantified according to the following formula:
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