CN104821875B - The high power capacity quantum secret sharing method realized based on photon trajectory angular momentum coding - Google Patents
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Abstract
The present invention realizes a kind of high power capacity quantum secret sharing method realized based on photon trajectory angular momentum coding, constructs two unitary operators, provides two groups of complete intrinsic quantum states；Annular quantum secret sharing communication is carried out, based on intrinsic quantum state space, sender Alice prepares photon sequence and issues Bob at random；Bob randomly selects verification photon from photon sequence and carried outOrMeasurement, is encoded, photon issues Charlie after coding according to key word string to remaining photon；Charlie carries out verification photon survey to the photon sequence of reception, remaining photon is encoded according to key word string, photon issues Alice after coding；Alice judges whether communication channel is safe, reads Bob and Charlie and combines carried out encoding operation.The present invention increases the message capacity and spectrum efficiency of quantum secret sharing scheme using single photon orbital angular momentum, it is not necessary to multicomponent entangled photons state.
Description
Technical field
The invention belongs to Technique on Quantum Communication field, and in particular to one kind is realized based on photon trajectory angular momentum higher-dimension coding
Quantum secret sharing method.
Background technology
Classical secret sharing scheme is realized in tripartite, wherein a side is as leading square, it is necessary to encryption key distribution
To two recipients, due to there may be a mistrustful side, so recipient needs to join together that encryption key could be read.
Existing quantum secret sharing scheme is that the polarization encoder based on single photon is realized.In order to realize that quantum secret information is shared, letter
The sender of breath by the use of two components or three component entangled photons as information bit, then by entangled photons by optical fiber or
Free space transmission, it is sent to recipient.Both sides pass through safety monitoring, then randomly choose measurement base.In tripartite's simultaneous selection
In the case of identical measuring basis, useful result can be obtained.Recipient, which combines the secret information respectively obtained, does XOR
Computing, you can the leading secret information just sent of generation.In traditional secret sharing scheme, what is utilized is the polarization freedom of photon
Degree, or on phase freedom, because the polarization free degree and phase freedom of photon are all two-dimensional encoded spaces, so coding
Capacity is limited to, so as to directly affects the rate of information throughput of quantum secret sharing.
Photon trajectory angular momentum be scientists in 1992 experiments prove that, it is theoretical for the electromagnetic wave of same frequency
On can have the values of infinite multiple different orbital angular momentums.In 2010, Lv Hong, Ke Xizheng was disclosed《Light beam orbit angular motion
The quantum communications coding method research of amount》, using high-order Bessel Beams there is orbital angular momentum to devise a kind of amount
Sub- encoding scheme.Disclose within 2012, Guo Jianjun, Guo Banghong, Cheng Guangming etc.《Photon trajectory angular momentum is applied in quantum communications
Progress》, the quantum-key distribution experimental program realized using photon trajectory angular momentum is described, is photon trajectory angular motion
The application measured in quantum communications provides thinking.At present, researcher has begun to utilize in quantum-key distribution scheme
Photon trajectory angular momentum conducts a research, and is realized and encoded using photon trajectory angular momentum, completes the safe transmission of key, but at present still
The problem of transmission capacity is low in right storage sub-secret secret sharing, and there is presently no be applied to quantum peace for orbital angular momentum
In full direct communication, the direct transmission of information is realized.
The content of the invention
It is an object of the invention to overcome the shortcomings of that transmission capacity is low in standing crop sub-secret secret sharing, design one
The high power capacity quantum secret sharing scheme that kind is realized information coding using photon trajectory angular momentum, decoded.
To realize object above, the invention provides a kind of high power capacity quantum realized based on photon trajectory angular momentum coding
Privacy sharing method, is realized especially by following steps：
Step 1：Carry out quantum state coding；
If the dimension of Higher Dimensional Metric subspace is p, the complete intrinsic quantum state of one of which be expressed as | 0>,|1>,...,
|p-1>, p is the integer more than 2；
Two unitary operators are constructed, are respectively：
Orbital angular momentum phase controlling operator in vector subspaceParameter ω=ei2π/p；
Orbital angular momentum size control operator in vector subspace
The concrete form of quantum state coding is constructed, is two groups of complete intrinsic quantum states, its form is expressed as：
{|t>, t=0,1,2 ..., p-1 } and | ψt>,
Wherein parameter sj=j+ (j+1)+...+(p-1), k represent any number in 0,1,2 ..., p-1.
In the high power capacity quantum secret sharing method of the present invention, quantum is recorded using the orbital angular momentum quantum state of photon
Operation information, quantum operation loading coding information is used as by the unitary operator of p dimension spaces.
Step 2：Annular quantum secret sharing communication is carried out, if communication tripartite is Alice, Bob and Charlie, wherein
Photon sequence is sent to Bob by Alice, and Charlie is sent to after Bob encoding operations, and Charlie encoding operations are sent later
To Alice；Before communication starts, dimensional space p is preselected, specific communication process includes step 2.1~step 2.4.
Here Alice is the leading side (Boss) in communication plan, and Bob and Charlie are the recipients of two information.
Step 2.1：After communication starts, the sender Alice of information randomly prepares one group of photon sequence, each light in it
Son orbital angular momentum state be at random intrinsic quantum state space | t>, t=0,1,2 ..., p-1 }, or | ψt>In；
The photon sequence of preparation is sent to Bob by Alice.
Step 2.2：After Bob receives a photon sequence, a part of photon is randomly selected from the photon sequence and is made
To verify photon, then the remaining photon that verification photon is removed in the photon sequence is photon to be encoded；Bob is random to verification photon
OrSpace measures；Then Bob treats coding photon and performed the encoding operation at random, will encode what is completed
Photon is sent to Charlie.
Bob is performed the encoding operation on photon to be encoded according to the key word string of oneself, is specifically：Treat coding photon
Orbital angular momentum, the h binary information sequences transmitted as needed, random selectionOrOperated, utilizedCodimg logic bit 0 is operated, is utilizedCodimg logic bit h is operated, whereinFor unit matrix, h value model
Enclose for (1,2 ..., p-1).
Step 2.3：Charlie selects one at random after the photon sequence after receiving Bob codings from the photon sequence
As verification photon, then the remaining photon that verification photon is removed in the photon sequence is photon to be encoded for part；Charlie is to school
Optometry exists at randomOrSpace measures；Then Charlie treats coding photon and performed the encoding operation at random,
The photon for encoding completion is sent to Alice.
Charlie is performed the encoding operation on photon to be encoded according to the key word string of oneself, treats the rail of coding photon
Road angular momentum, the h binary information sequences transmitted as needed, random selectionOrOperated, utilized
Codimg logic bit 0 is operated, is utilizedOperate codimg logic bit h.
Step 2.4：After Alice receives photon sequence, pass through overt channel Inspection light with Bob, Charlie respectively
Position, measurement base and the measurement result of son, judge whether bit error rate is less than the secure threshold of communication channel, if so, then leading to
Believe that channel is safe, otherwise communication channel is dangerous.
When communication channel is safe, Alice contrast photon trajectory angular momentum original state and end-state, read Bob and
Charlie combines carried out encoding operation, and Alice key is the product of Bob and Charlie coded key；Communication letter
When road is dangerous, stop communication.
Relative to prior art, the advantages and positive effects of the present invention are：
(1) quantum information that photon trajectory angular momentum is realized using hologram sheet and linear optical element is coded and decoded；
(2) the higher-dimension quantum secret sharing of the annular distribution mode based on photon trajectory angular momentum is realized, utilizes monochromatic light
Sub-track angular momentum increases the message capacity and spectrum efficiency of quantum secret sharing scheme；
(3) space encoder of secret information is expanded to N-dimensional system by the present invention, in the orbital angular momentum space of single photon
The quantum secret sharing scheme of this annular distribution mode is realized, its is more efficient, it is not necessary to multicomponent entangled photons state, therefore
Realizability is stronger.
Brief description of the drawings
Fig. 1 is the schematic diagram of orbital angular momentum separator；
Fig. 2 is that the quantum secret sharing method of the invention based on orbital angular momentum is illustrated in the code device of quintuple space
Figure；
Fig. 3 is communication tripartite's schematic diagram of the quantum secret sharing method of the invention based on orbital angular momentum；
Fig. 4 is the schematic flow sheet of the quantum secret sharing method of the invention based on orbital angular momentum.
Embodiment
Below in conjunction with drawings and examples, the present invention is described in further detail.
The core of the present invention is that this electromagnetic wave parameter dimensions is used for quantum secret sharing side the orbital angular momentum of photon
In case, the spectrum communication efficiency and capacity of quantum secret sharing system are improved using photon trajectory angular momentum.
Fig. 1 is orbital angular momentum separator, it is possible to achieve manipulation of the orbital angular momentum in two-dimensional space.In Fig. 1：CPBS tables
Show circularly polarized light polarization beam splitter, PBS represents polarised light polarization beam splitter, and R represents speculum, and DP represents Dove prisms.Track
Angular momentum separator entrance port photonic quantum state can mark forWherein | H>Represent that the polarization of photon is in level
The state of polarization, | l>The value for representing the orbital angular momentum of this photon is l.When photon is after CPBS devices, its left-handed and dextrorotation
The component of circular polarization will be separated, and its left-handed photon states will be by path 1, and its dextrorotation photon states will be by path 2.
Path 1 refers to be connected to the path on the right side of CPBS devices in Fig. 1, successively through DP and R, arrival PBS on path 1.Road
Footpath 2 refers to connect the path below CPBS devices in Fig. 1, successively through R and DP, arrival PBS on path 2.
Dove prism optical axises in device on path 1 and path 2 have a relative α differential seat angle, two-way circularly polarized light point
Not Jing Guo Dove prisms and being merged into by PBS export all the way, final state is changed into：
It is α=(pi/2)/(l that suitable α values, which can be adjusted,1-l2), two states of photon can be obtained eventually through two ports of PBS
Component, it is respectively：WithWherein l=(l1+l2)。l1And l2The track angular motion of respectively two photons
Numerical quantity, it is the positive integer less than l.
The inventive method based on device include coding module and decoder module, coding module is as shown in Fig. 2 and decode mould
Block is the inverse process of coding module.Embodiment illustrated in fig. 2 is communicated in dimension p=5 vector subspace, sender's cascade
5 Fig. 1 devices, the orbital angular momentum separator by cascade, different orbital angular momentum l photon component will be along difference
Path output, path here marks different orbital angular momentum values successively from top to bottom.In embodiment illustrated in fig. 2：ω0~
ω4The different path frees degree is represented successively, Cascaded OAM sorter represent the orbital angular momentum separator of cascade,
Reversed configuration expressions are the inverse process of OAM sorter cascade units.Per on the way, can carry out
Or/andOperation, whereinIt is phase-shift operations, can be completed by phase plate；It is quarter-wave plate and hologram sheet
Collective effect complete, it is possible to achieve the conversion between different orbital angular momentum quantum states.
The annular quantum secret sharing method based on photon trajectory angular momentum coding of the present invention, the device being based on include
The realization of coding module and decoder module, wherein coding module is as shown in Fig. 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, with reference to Fig. 3 and
Fig. 4, each step is described as follows.
Step 1：Carry out quantum state coding.
If the dimension of Higher Dimensional Metric subspace is p, the complete intrinsic quantum state of one of which can be expressed as | 0>,|1
>,...,|p-1>, p is the natural number more than 2.
In this vector subspace, two unitary operators can be constructed, its concrete form is：
And
Wherein, j values are less than p natural number, for representing the state of photon trajectory angular momentum.
The angular momentum phase controlling operator in vector subspace is represented,Represent the angular momentum size control in vector subspace
Operator processed.WhereinThe phase of the orbital angular momentum of specific photon can be changed,The orbital angular momentum of photon can be changed
Size；Parameter ω=ei2π/p。
Further, the concrete form of coding state is constructed, space encoder is tieed up for p, and coding state is two groups of complete intrinsic quantums
State, its form can be expressed as | t>, t=0,1,2 ..., p-1 } and | ψt>, here
Wherein parameter sj=j+ (j+1)+...+(p-1), t=0, wherein 1,2 ..., p-1, superscript k are represented in 0,1,2 ..., p-1
Any number.
In the methods of the invention, the information that will be transmitted is encoded on quantum state, is completed by the unitary operator of p dimension spaces
Encoding operation.
Step 2：Carry out annular quantum secret sharing.
It is the principle of the annular quantum secret sharing of the present invention shown in Fig. 3 if the tripartite that communicates is Alice, Bob and Charlie
Photon sequence is sent to Bob by figure, information source Alice, and Charlie is sent to after the encoded operations of Bob, and Charlie is compiled
Alice is sent to after code operation, so as to form a circular communication pattern.
Step 2.1：Communicate the preselect dimensional space p of tripartite Alice, Bob and Charlie；P is whole more than 2
Number.After communication starts, Alice randomly prepares one group of photon sequence, and photon sequence includes n photon, the quantum of each photon
State isThe photon sequence of preparation is sent to Bob by Alice by quantum channel.
The orbital angular momentum state of each photon in photon sequence prepared by Alice, random is inOrIntrinsic quantum state space | t>, t=0,1,2 ..., p-1 }, or | ψt>In.
Step 2.2：Bob randomly selects one after the photon sequence that Alice is sent is received from the photon sequence
As verification photon, then the remaining photon that verification photon is removed in the photon sequence is Bob photon to be encoded for part.Verify light
Son is for carrying out safety detection.Bob is carried out using the device shown in Fig. 2 to verification photon on pathOr/andMeasurement, obtain verify photon measurement result；After measurement terminates, Bob is on photon to be encoded according to the key word of oneself
String kBPerform the encoding operation, the photon for completing encoding operation is sent to Charlie by Bob.
Specific coding operates：Treat coding photon orbital angular momentum, the h binary information sequences transmitted as needed,
Random selectionOrOperated, utilizedCodimg logic bit 0 is operated,For unit matrix, represent not
Do any operation；UtilizeCodimg logic bit h is operated, wherein h span is (1,2 ..., p-1).For example,
The orbital angular momentum of photon is | ψt>, codimg logic bit h is operated, can be expressed as in mathematical formDirectly multiply
With | ψt>。
P=5 in the embodiment of the present invention, as shown in Fig. 2 Bob cascades the orbital angular momentum separator shown in p Fig. 1, verification
Orbital angular momentum separator of the photon through p cascade, the photon component of the different orbital angular momentum values of output are defeated along different paths
Go out, mark has the orbital angular momentum value ω of the output after being operated in orbital angular momentum separator on pathj.Each
In orbital angular momentum separator corresponding to paths, carry out correspondingOr/andOperation, whereinOperation passes through phase shift
Piece is completed,Operation is realized by quarter-wave plate and hologram sheet collective effect.
Verification photon does not need encoding operation, is to obtain the orbital angular momentum of photon to verification photon survey, carries out
Safety detection.
Step 2.3：Charlie repeats Bob operating process, to receiving after the photon sequence that Bob is sent is received
Photon sequence encoded after be sent to Alice.
Charlie is similar with Bob after the photon sequence that Bob is sent is received, and is randomly selected from photon sequence
For a part of photon as verification photon, then the remaining photon that verification photon is removed in the photon sequence is the to be encoded of Charlie
Photon.Charlie, using the orbital angular momentum separator of the device shown in Fig. 2 on each path, randomly enters to verifying photon
OKOrMeasurement, obtain verify photon orbital angular momentum state.
After measurement terminates, Charlie is on photon to be encoded according to the key word string k of oneselfCPerform the encoding operation.
Cataloged procedure is identical with Bob operation, the h binary information sequences transmitted as needed, the track angular motion to photon
Amount, is randomly selectedOrOperated, utilizedCodimg logic bit 0 is operated, is utilizedOperation is compiled
Code logical bits h.
Encoded photon is sent back into Alice after Charlie completion encoding operations.
Step 2.4：After Alice receives photon, pass through overt channel Inspection photon with Bob, Charlie respectively
Position, measurement base and measurement result, carry out communication channel safety verification.When communication channel is safe, Alice contrast photon trajectories
The original state and end-state of angular momentum, read Bob and Charlie and combine carried out encoding operation.When communication channel not
When safe, stop communication.
After Alice receives photon, by the overt channel position with Bob and Charlie Inspection photons respectively, survey
Measure base and measurement result.According to measurement result, judge whether bit error rate is less than the secure threshold of channel, if being less than, then
It is safe that communication channel, which can be determined, and otherwise, communication channel is dangerous.
Because Alice is the preparation person of bit, so the initial track angular motion for knowing each photon that Alice is determined
Amount state.Selected when Alice is prepared according to photon intrinsic quantum state space | t>, t=0,1,2 ..., p-1 } or | ψt
>, the measurement of orbital angular momentum is carried out in intrinsic quantum state space to the photon received, so as to read the final of photon
Orbital angular momentum state.The preliminary orbit angular momentum state and last turn angular momentum state of photon are contrasted, Alice can be read
Go out Bob and Charlie and combine carried out encoding operation, that is, read out Bob and Charlie coded key
So as to construct key bit information.So far, secret sharing scheme is completed, and Alice key is Bob and Charlie coding
The product of key.
Claims (2)
- A kind of 1. high power capacity quantum secret sharing method realized based on photon trajectory angular momentum coding, it is characterised in that utilize Orbital angular momentum quantum state encodes, realize high power capacity quantum secret information it is shared, comprise the following steps：Step 1：Carry out quantum state coding；If the dimension of Higher Dimensional Metric subspace is p, p is the integer more than 2；Construct the orbital angular momentum phase controlling operator in vector subspaceParameter ω=ei2π/p, ω expressions The path free degree；Construct the orbital angular momentum size control operator in vector subspaceThe concrete form of quantum state coding is constructed, is two groups of complete intrinsic quantum states, its form is expressed as：{|t>, t=0,1,2 ..., p-1 } and | ψt>}；Wherein,Parameter sj=j+ (j+1)+...+(p-1), k represent 0,1,2 ..., p-1 Middle any number；Step 2：Annular quantum secret sharing communication is carried out, if communication tripartite is Alice, Bob and Charlie, wherein Alice will Photon sequence is sent to Bob, and Charlie is sent to after the encoded operations of Bob, and Charlie encoding operations are sent to later Alice；Before communication starts, dimensional space p is preselected, specific communication process includes step 2.1~step 2.4；Step 2.1：Alice randomly prepares one group of photon sequence, and orbital angular momentum state of each photon is at random in it Intrinsic quantum state spaceOrIn；The photon sequence of preparation is sent to Bob by Alice；Step 2.2：After Bob receives photon sequence, a part of photon is randomly selected from the photon sequence as verification light Son, then the remaining photon that verification photon is removed in the photon sequence is photon to be encoded；Bob exists at random to verification photonOr/ WithSpace measures, and obtains verifying the orbital angular momentum state of photon；Then Bob treats coding photon and compiled at random Code operation, the photon for encoding completion is sent to Charlie；Bob is performed the encoding operation on photon to be encoded according to the key word string of oneself, is specifically：Treat the track of coding photon Angular momentum, the h binary information sequences transmitted as needed, random selectionOrOperated, utilizedOperation Codimg logic bit 0, utilizeCodimg logic bit h is operated, whereinFor unit matrix, h span for (1, 2 ..., p-1)；Step 2.3：Charlie selects a part at random after the photon sequence after receiving Bob codings from the photon sequence As verification photon, then the remaining photon that verification photon is removed in the photon sequence is photon to be encoded；Charlie exists at random to verification photonOr/andSpace measures；Then it is random to treat coding photon by Charlie Perform the encoding operation, the photon for encoding completion is sent to Alice；Charlie is performed the encoding operation on photon to be encoded according to the key word string of oneself, treats the track angle of coding photon Momentum, the h binary information sequences transmitted as needed, random selectionOrOperated, utilizedOperation is compiled Code logical bits 0, are utilizedOperate codimg logic bit h；Step 2.4：After Alice receives photon sequence, pass through overt channel Inspection photon with Bob, Charlie respectively Position, measurement base and measurement result, judge whether bit error rate is less than the secure threshold of communication channel, if so, then communication letter Road is safe, and otherwise communication channel is dangerous；When communication channel is safe, Alice contrast photon trajectory angular momentum original state and end-state, read Bob and Charlie combines carried out encoding operation, and Alice key is the product of Bob and Charlie coded key；Communication letter When road is dangerous, stop communication.
- 2. the high power capacity quantum secret sharing method according to claim 1 realized based on photon trajectory angular momentum coding, Characterized in that, described sender Alice, cascades p orbital angular momentum separator, p rail of the photon by cascade is verified Road angular momentum separator, it is random to carry outOr/andOperation, whereinOperation is completed by phase plate,Operation passes through four / mono- wave plate and hologram sheet collective effect are realized；The photon component of the different orbital angular momentum values of output is defeated along different paths Go out, mark has orbital angular momentum value ω on pathj。
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| CN115545207A (en) | 2015-12-30 | 2022-12-30 | 谷歌有限责任公司 | Quantum phase estimation of multiple eigenvalues |
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| CN106899970B (en) * | 2017-01-21 | 2020-03-31 | 西北工业大学 | Wireless communication encryption method based on angular momentum |
| WO2020262743A1 (en) * | 2019-06-28 | 2020-12-30 | 엘지전자 주식회사 | Method for transmitting and receiving signal in optical wireless communication system, and transmission terminal and reception terminal therefor |
| CN111865577B (en) * | 2020-07-08 | 2021-10-08 | 西南大学 | Quantum key distribution method and quantum communication system |
| CN117014142B (en) * | 2023-10-07 | 2023-12-15 | 山东高速建设管理集团有限公司 | Semi-quantum secret sharing method based on ring-shaped transmission mode |
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