CN104821875A - High-capacity quantum secret sharing method based on photon orbit angular momentum coding - Google Patents
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Abstract
The invention discloses a high-capacity quantum secret sharing method based on photon orbit angular momentum coding. The method comprises the steps: constructing two unitary operators; giving two groups of complete intrinsic quantum states; carrying out annular quantum secret sharing communication. Based on an intrinsic quantum state space, transmitter side Alice randomly prepares a photon sequence and transmits the photon sequence to Bob. Bob randomly selects verification photons from the photon sequence for measurement described in the specification. The coding of the residual photons is carried out according to a secret key character string, and the coded photons are transmitted to Charlie. Charlie carries out measurement of photon verification of the received photon sequence, and codes the residual photons according to the secret key character string, and transmits the coded photons to Alice. Alice judges whether a communication channel is safe or not, and reads the coding operation which is carried out by Bob and Charlie jointly. The method employs single-photon orbit angular momentum coding to improve the communication capacity and frequency spectrum efficiency of a quantum secret sharing scheme, and does not need multicomponent entangled photon states.
Description
Technical field
The invention belongs to Technique on Quantum Communication field, be specifically related to a kind of quantum secret sharing method realized based on photon trajectory angular momentum higher-dimension coding.
Background technology
Classical secret sharing scheme realizes tripartite, and wherein a side is as leading side, needs encryption key distribution to two recipients, owing to may there is a mistrustful side, so recipient needs to join together to read encryption key.Existing quantum secret sharing scheme realizes based on the polarization encoder of single photon.Share to realize quantum secret information, the sender of information utilizes two components or three components entangled photons as information bit, then entangled photons is passed through optical fiber or free space transmission, sends to recipient.Both sides, through safety monitoring, then choose measurement base randomly.When tripartite selects identical measuring basis simultaneously, useful result can be obtained.The secret information obtained respectively is combined and is done XOR by recipient, can generate the secret information that leading side sends.In traditional secret sharing scheme, what utilize is the polarization degree of freedom of photon, or on phase freedom, because the polarization degree of freedom of photon and phase freedom are all two-dimensional encoded spaces, so code capacity is limited to, thus directly affects the rate of information throughput of quantum secret sharing.
Photon trajectory angular momentum is that scientist in 1992 confirms by experiment, for the electromagnetic wave of same frequency, can have the value of infinite multiple different orbital angular momentum in theory.In 2010, Lv Hong, Ke Xizheng disclosed " the quantum communications coding method research of light beam orbit angular momentum ", utilize high-order Bessel Beams to have orbital angular momentum and devise a kind of quantum coding scheme.2012, Guo Jianjun, Guo Banghong, Cheng Guangming etc. disclose " progress that photon trajectory angular momentum is applied in quantum communications ", describe the quantum-key distribution experimental program utilizing photon trajectory angular momentum to realize, for the application of photon trajectory angular momentum in quantum communications provides thinking.At present, researcher has started to utilize photon trajectory angular momentum to conduct a research in quantum-key distribution scheme, photon trajectory angular momentum is utilized to realize coding, complete the safe transmission of key, but the problem that in the current still sub-secret sharing scheme of storage, transmission capacity is low, and orbital angular momentum is not also applied in Quantum Secure Direct Communication at present, realizes the direct transmission of information.
Summary of the invention
The object of the invention is to overcome the deficiency that in existing quantum secret sharing scheme, transmission capacity is low, design a kind of high power capacity quantum secret sharing scheme utilizing photon trajectory angular momentum to realize information coding, decoding.
For realizing above object, the invention provides a kind of high power capacity quantum secret sharing method realized based on photon trajectory angular momentum coding, realizing especially by following steps:
Step 1: carry out quantum state coding;
If the dimension of Higher Dimensional Metric subspace is p, wherein one group of complete intrinsic quantum state be expressed as | 0>, | 1> ..., | p-1>}, p be greater than 2 integer;
Construct two unitary operators, respectively:
Orbital angular momentum phase control operator in vector subspace
parameter ω=e
i2 π/p;
Orbital angular momentum size in vector subspace controls operator
The concrete form of structure quantum state coding, be two groups of complete intrinsic quantum states, its form is expressed as:
| t>, t=0,1,2 ..., p-1} and | ψ
t>},
Wherein parameter s
j=j+ (j+1)+...+(p-1), k represents 0,1,2 ..., any number in p-1.
In high power capacity quantum secret sharing method of the present invention, utilize the orbital angular momentum quantum state recorded amounts child-operation information of photon, load coded message by the unitary operator of p dimension space as quantum operation.
Step 2: carry out annular quantum secret sharing communication, if communication tripartite is Alice, Bob and Charlie, wherein photon sequence is sent to Bob by Alice, and Bob encoding operation sends to Charlie later, and Charlie encoding operation sends to Alice later; Before communication starts, chosen in advance dimensional space p, concrete communication process comprises step 2.1 ~ step 2.4.
Here Alice is the leading side (Boss) in communication plan, and Bob and Charlie is the recipient of two information.
Step 2.1: communication start after, the transmit leg Alice of information prepares one group of photon sequence randomly, in it orbital angular momentum state of each photon be at random intrinsic quantum state space | t>, t=0,1,2 ..., p-1}, or | ψ
tin >}; The photon sequence of preparation is sent to Bob by Alice.
After step 2.2:Bob receives a photon sequence, select a part of photon randomly as verification photon from this photon sequence, then in this photon sequence, the residue photon of removing verification photon is photon to be encoded; Bob exists at random to verification photon
or
space is measured; Then Bob treat coding photon carry out encoding operation at random, the photon of having encoded is sent to Charlie.
The key word string of Bob according to oneself on photon to be encoded carries out encoding operation, specifically: the orbital angular momentum treating coding photon, the h binary information sequence transmitted as required, random chooses
or
operate, utilize
operate coding logical bits 0, utilizes
operate coding logical bits h, wherein
for unit matrix, the span of h be (1,2 ..., p-1).
After the photon sequence of step 2.3:Charlie after receiving Bob coding, select a part at random as verification photon from this photon sequence, then in this photon sequence, the residue photon of removing verification photon is photon to be encoded; Charlie exists at random to verification photon
or
space is measured; Then Charlie treat coding photon carry out encoding operation at random, the photon of having encoded is sent to Alice.
The key word string of Charlie according to oneself on photon to be encoded carries out encoding operation, and treat the orbital angular momentum of coding photon, the h binary information sequence transmitted as required, random chooses
or
operate, utilize
operate coding logical bits 0, utilizes
operate coding logical bits h.
After step 2.4:Alice receives photon sequence, pass through the position of overt channel Inspection photon respectively with Bob, Charlie, measure base and measurement result, judge bit error rate whether lower than the secure threshold of communication channel, if, then communication channel is safe, otherwise communication channel is dangerous.
When communication channel is safe, Alice contrasts initial condition and the end-state of photon trajectory angular momentum, and read Bob and Charlie and combine the encoding operation carried out, the key of Alice is the product of the coded key of Bob and Charlie; When communication channel is dangerous, stop communication.
Relative to prior art, advantage of the present invention and good effect are:
(1) hologram sheet and linear optical element is utilized to achieve the quantum information Code And Decode of photon trajectory angular momentum;
(2) achieve the higher-dimension quantum secret sharing of the annular distribution mode based on photon trajectory angular momentum, utilize single photon orbital angular momentum to increase message capacity and the spectrum efficiency of quantum secret sharing scheme;
(3) space encoder of secret information is expanded to N and ties up system by the present invention, the quantum secret sharing scheme of this annular distribution mode is achieved in the orbital angular momentum space of single photon, its efficiency is higher, do not need multicomponent entangled photons state, therefore realizability is stronger.
Accompanying drawing explanation
Fig. 1 is the schematic diagram of orbital angular momentum separator;
Fig. 2 is the quantum secret sharing method that the present invention is based on orbital angular momentum code device schematic diagram at quintuple space;
Fig. 3 is the communication tripartite schematic diagram of the quantum secret sharing method that the present invention is based on orbital angular momentum;
Fig. 4 is the schematic flow sheet of the quantum secret sharing method that the present invention is based on orbital angular momentum.
Embodiment
Below in conjunction with drawings and Examples, the present invention is described in further detail.
Core of the present invention be this electromagnetic wave parameter dimensions of the orbital angular momentum of photon in quantum secret sharing scheme, utilize photon trajectory angular momentum to improve spectrum communication efficiency and the capacity of quantum secret sharing systems.
Fig. 1 is orbital angular momentum separator, can realize the manipulation of orbital angular momentum at two-dimensional space.In Fig. 1: CPBS represents circularly polarized light polarization beam splitter, PBS represents polarised light polarization beam splitter, and R represents speculum, and DP represents Dove prism.Orbital angular momentum separator entrance port photonic quantum state can be labeled as
wherein | H> represents that the polarization of photon is in the state of horizontal polarization, | l> represents that the value of the orbital angular momentum of this photon is l.When photon is after CPBS device, its left-handed and component that is right-hand circular polarization is opened separated, and its left-handed photon states will through path 1, and its dextrorotation photon states will through path 2.Path 1 refers in Fig. 1 the path be connected on the right side of CPBS device, successively through a DP and R on path 1, arrives PBS.Path 2 refers in Fig. 1 the path connected below CPBS device, successively through a R and DP on path 2, arrives PBS.
In device, path 1 and the Dove prism optical axis on path 2 have a relative α differential seat angle, and two-way circularly polarized light is respectively through Dove prism and be merged into a road by PBS and export, and final state becomes:
suitable α value can be adjusted for α=(pi/2)/(l
1-l
2), two state components of photon can be obtained eventually through PBS two ports, be respectively:
with
wherein l=(l
1+ l
2).L
1and l
2be respectively the orbital angular momentum numerical value of two photons, be the positive integer being less than l.
The inventive method based on device comprise coding module and decoder module, as shown in Figure 2, and decoder module is the inverse process of coding module to coding module.Embodiment illustrated in fig. 2 is communicate in the vector subspace of dimension p=5, transmit leg cascade 5 Fig. 1 devices, through the orbital angular momentum separator of cascade, the photon component of different orbital angular momentum l exports along different paths, and path here marks different orbital angular momentum values from top to bottom successively.In embodiment illustrated in fig. 2: ω
0~ ω
4represent the different path degrees of freedom successively, Cascaded OAM sorter represents the orbital angular momentum separator of cascade, and Reversedconfiguration represents it is the inverse process of OAM sorter cascade unit.Often on the way, can carry out
or/and
operation, wherein
be phase-shift operations, can be completed by phase plate;
be that the acting in conjunction of quarter-wave plate and hologram sheet completes, the conversion between different orbital angular momentum quantum state can be realized.
Of the present invention based on photon trajectory angular momentum coding annular quantum secret sharing method, based on device comprise coding module and decoder module, wherein the realization of coding module is as shown in Figure 2, and decoder module is the inverse process of coding module.
The high power capacity quantum secret sharing method realized based on photon trajectory angular momentum coding of the present invention, composition graphs 3 and Fig. 4, be described as follows each step.
Step 1: carry out quantum state coding.
If the dimension of Higher Dimensional Metric subspace is p, wherein one group of complete intrinsic quantum state can be expressed as | 0>, | 1> ..., | p-1>}, p be greater than 2 natural number.
In this vector subspace, can construct two unitary operators, its concrete form is:
Wherein, j value is the natural number being less than p, for representing the state of photon trajectory angular momentum.
represent the angular momentum phase control operator in vector subspace,
represent that the angular momentum size in vector subspace controls operator.Wherein
the phase place of the orbital angular momentum of specific photon can be changed,
the size of the orbital angular momentum of photon can be changed; Parameter ω=e
i2 π/p.
Further, construct the concrete form of coding state, space encoder is p dimension, and coding state is two groups of complete intrinsic quantum states, its form can be expressed as | t>, t=0,1,2 ..., p-1} and | ψ
t>}, here
wherein parameter s
j=j+ (j+1)+...+(p-1), t=0,1,2 ..., p-1, wherein superscript k represents 0,1,2 ..., any number in p-1.
In the methods of the invention, the information coding that will transmit, on quantum state, completes encoding operation by the unitary operator of p dimension space.
Step 2: carry out annular quantum secret sharing.
If communication tripartite is Alice, Bob and Charlie, it is the schematic diagram of the present invention's annular quantum secret sharing shown in Fig. 3, photon sequence is sent to Bob by information source Alice, Bob sends to Charlie after encoding operation, Charlie encoding operation sends to Alice later, thus forms a circular communication pattern.
Step 2.1: communication tripartite's Alice, Bob and Charlie chosen in advance dimensional space p; P be greater than 2 integer.After communication starts, Alice prepares one group of photon sequence randomly, and photon sequence comprises n photon, and the quantum state of each photon is
the photon sequence of preparation is sent to Bob by Alice throughput subchannel.
The orbital angular momentum state of each photon in the photon sequence prepared by Alice, random is in
or
intrinsic quantum state space | t>, t=0,1,2 ..., p-1}, or | ψ
tin >}.
Step 2.2:Bob, after receiving the photon sequence that Alice sends, selects a part randomly as verification photon from this photon sequence, then in this photon sequence, the residue photon of removing verification photon is the photon to be encoded of Bob.Verification photon is used to carry out fail safe detection.Bob uses the device shown in Fig. 2, carries out on path verification photon
or/and
measurement, obtain verifying the measurement result of photon; After measurement terminates, Bob on photon to be encoded according to the key word string k of oneself
bcarry out encoding operation, the photon completing encoding operation is sent to Charlie by Bob.
Specific coding operation is: the orbital angular momentum treating coding photon, the h binary information sequence transmitted as required, random chooses
or
operate, utilize
operate coding logical bits 0,
for unit matrix, represent and do not do any operation; Utilize
operate coding logical bits h, wherein the span of h be (1,2 ..., p-1).Such as, the orbital angular momentum of photon is | ψ
t>, operate coding logical bits h, mathematical form can be expressed as
directly be multiplied by | ψ
t>.
P=5 in the embodiment of the present invention, as shown in Figure 2, orbital angular momentum separator shown in Bob cascade p Fig. 1, verification photon is through the orbital angular momentum separator of p cascade, the photon component of the different orbital angular momentum values exported exports along different path, and path is marked with the orbital angular momentum value ω of corresponding output in orbital angular momentum separator after operation
j.In the orbital angular momentum separator that each paths is corresponding, carry out corresponding
or/and
operation, wherein
operation is completed by phase plate,
operate and realized by quarter-wave plate and hologram sheet acting in conjunction.
Verification photon does not need encoding operation, being the orbital angular momentum in order to obtain photon, carrying out fail safe detection to verification photon survey.
Step 2.3:Charlie, after receiving the photon sequence that Bob sends, repeats the operating process of Bob, sends to Alice after encoding to the photon sequence received.
Charlie is after receiving the photon sequence that Bob sends, similar with Bob, selects a part of photon randomly as verification photon from photon sequence, then in this photon sequence, the residue photon of removing verification photon is the photon to be encoded of Charlie.Charlie, to verification photon, uses the orbital angular momentum separator on each path of the device shown in Fig. 2, carries out randomly
or
measurement, obtain verifying the orbital angular momentum state of photon.
After measurement terminates, Charlie on photon to be encoded according to the key word string k of oneself
ccarry out encoding operation.
Cataloged procedure is identical with the operation of Bob, the h binary information sequence transmitted as required, to the orbital angular momentum of photon, and random selecting
or
operate, utilize
operate coding logical bits 0, utilizes
operate coding logical bits h.
After Charlie completes encoding operation, encoded photon is sent back to Alice.
After step 2.4:Alice receives photon, pass through the position of overt channel Inspection photon respectively with Bob, Charlie, measure base and measurement result, carry out communication channel safety verification.When communication channel is safe, Alice contrasts initial condition and the end-state of photon trajectory angular momentum, reads Bob and Charlie and combines the encoding operation carried out.When communication channel is dangerous, stop communication.
After Alice receives photon, by overt channel respectively with the position of Bob and Charlie Inspection photon, measure base and measurement result.According to measurement result, judge bit error rate whether lower than the secure threshold of channel, if lower than, so can determine that communication channel is safe, otherwise communication channel is dangerous.
Due to the preparation person that Alice is bit, so the initial orbital angular momentum state knowing each photon that Alice determines.When Alice is prepared according to photon select intrinsic quantum state space | t>, t=0,1,2 ..., p-1} or | ψ
t>}, carries out the measurement of orbital angular momentum in intrinsic quantum state space to the photon received, thus reads the final orbital angular momentum state of photon.The preliminary orbit angular momentum state of contrast photon and last turn angular momentum state, namely Alice can read Bob and Charlie and combine the encoding operation carried out, and namely reads out the coded key of Bob and Charlie
thus construct key bit information.So far, secret sharing scheme completes, and the key of Alice is the product of the coded key of Bob and Charlie.
Claims (2)
1. based on the high power capacity quantum secret sharing method that photon trajectory angular momentum coding realizes, it is characterized in that, utilize orbital angular momentum quantum state to encode, realize sharing of the quantum secret information of high power capacity, comprise the steps:
Step 1: carry out quantum state coding;
If the dimension of Higher Dimensional Metric subspace is p, p be greater than 2 integer;
Orbital angular momentum phase control operator in structure vector subspace
parameter ω=e
i2 π/p;
Orbital angular momentum size in structure vector subspace controls operator
The concrete form of structure quantum state coding, be two groups of complete intrinsic quantum states, its form is expressed as:
| t>, t=0,1,2 ..., p-1} and { ψ
t>};
Wherein,
parameter s
j=j+ (j+1)+...+(p-1), k represents 0,1,2 ..., any number in p-1;
Step 2: carry out annular quantum secret sharing communication, if communication tripartite is Alice, Bob and Charlie, wherein photon sequence is sent to Bob by Alice, and Bob sends to Charlie after encoding operation, and Charlie encoding operation sends to Alice later; Before communication starts, chosen in advance dimensional space p, concrete communication process comprises step 2.1 ~ step 2.4;
Step 2.1:Alice prepares one group of photon sequence randomly, in it orbital angular momentum state of each photon be at random intrinsic quantum state space | t>, t=0,1,2 ..., p-1} or | ψ
tin >}; The photon sequence of preparation is sent to Bob by Alice;
After step 2.2:Bob receives photon sequence, select a part of photon randomly as verification photon from this photon sequence, then in this photon sequence, the residue photon of removing verification photon is photon to be encoded; Bob exists at random to verification photon
or/and
space is measured, and obtains the orbital angular momentum state verifying photon; Then Bob treat coding photon carry out encoding operation at random, the photon of having encoded is sent to Charlie;
The key word string of Bob according to oneself on photon to be encoded carries out encoding operation, specifically: the orbital angular momentum treating coding photon, the h binary information sequence transmitted as required, random chooses
or
operate, utilize
operate coding logical bits 0, utilizes
operate coding logical bits h, wherein
for unit matrix, the span of h be (1,2 ..., p-1);
After the photon sequence of step 2.3:Charlie after receiving Bob coding, select a part at random as verification photon from this photon sequence, then in this photon sequence, the residue photon of removing verification photon is photon to be encoded;
Charlie exists at random to verification photon
or/and
space is measured; Then Charlie treat coding photon carry out encoding operation at random, the photon of having encoded is sent to Alice;
The key word string of Charlie according to oneself on photon to be encoded carries out encoding operation, and treat the orbital angular momentum of coding photon, the h binary information sequence transmitted as required, random chooses
or
operate, utilize
operate coding logical bits 0, utilizes
operate coding logical bits h;
After step 2.4:Alice receives photon sequence, pass through the position of overt channel Inspection photon respectively with Bob, Charlie, measure base and measurement result, judge bit error rate whether lower than the secure threshold of communication channel, if, then communication channel is safe, otherwise communication channel is dangerous;
When communication channel is safe, Alice contrasts initial condition and the end-state of photon trajectory angular momentum, and read Bob and Charlie and combine the encoding operation carried out, the key of Alice is the product of the coded key of Bob and Charlie; When communication channel is dangerous, stop communication.
2. the high power capacity quantum secret sharing method realized based on photon trajectory angular momentum coding according to claim 1, it is characterized in that, described transmit leg Alice, a cascade p orbital angular momentum separator, verification photon, by p orbital angular momentum separator of cascade, carries out at random
or/and
operation, wherein
operation is completed by phase plate,
operate and realized by quarter-wave plate and hologram sheet acting in conjunction; The photon component of the different orbital angular momentum values exported exports along different path, path is marked with corresponding orbital angular momentum value ω
j.
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