CN107332628A - Computer coding method based on quantum entanglement and least square method - Google Patents

Computer coding method based on quantum entanglement and least square method Download PDF

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CN107332628A
CN107332628A CN201710541311.2A CN201710541311A CN107332628A CN 107332628 A CN107332628 A CN 107332628A CN 201710541311 A CN201710541311 A CN 201710541311A CN 107332628 A CN107332628 A CN 107332628A
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CN107332628B (en
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刘嘉辉
董强
宋大华
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Harbin University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/24—Testing correct operation
    • H04L1/245—Testing correct operation by using the properties of transmission codes
    • H04L1/246—Testing correct operation by using the properties of transmission codes two-level transmission codes, e.g. binary
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/70—Photonic quantum communication
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/80—Optical aspects relating to the use of optical transmission for specific applications, not provided for in groups H04B10/03 - H04B10/70, e.g. optical power feeding or optical transmission through water
    • H04B10/85—Protection from unauthorised access, e.g. eavesdrop protection

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Abstract

The present invention provides a kind of information transferring method of the computer code based on quantum entanglement and least square method, including：One group of constraints that transmitting terminal and receiving terminal are observed jointly, each binary bit of information is expressed as quantum entanglement form, adjacent binary bit of information is in Quantum Entangled States, transmitting terminal is encoded according to quantum entanglement to the binary message for needing to transmit, transmitting terminal is as needed using one-to-one, one-to-many form is transmitted, and receiving terminal is measured and decoded according to constraints, realizes that information bit correctly judges.The present invention realizes the coding of the binary message of computer by quantum entanglement principle, overcomes influence of the fragility of the quantum entanglement in actual measurement to quantum coding and quantum calculation etc..The present invention determines the position relationship of binary message by least square method, and the judgement of quantum entanglement condition is optimized by probabilistic method, the basic demand of binary information transmission in quantum calculation and quantum coding is disclosure satisfy that.

Description

Computer coding method based on quantum entanglement and least square method
Technical field
The present invention relates to quantum calculation and computerized information coding techniques field, more particularly to it is a kind of based on quantum entanglement and The computer coding method of least square method.
Background technology
Quantum（Quantum）It is the key concept of modern physicses, is can show something or physics flow characteristic basic Unit.It is to be proposed by roentgen M.Planck in 1900 earliest.Quantum mainly shows the spy in the microphysics world Point, has very big difference with the classical physics of newton.Quantum mechanics by A.Einstein, N.Bohr, L.de Broglie, W.Heisenberg, E.Schr dinger, P.Dirac, M.Born et al. constantly improve, it is preliminary in the first half in 20th century Establish complete quantum-mechanical theory.
Quantum entanglement（Quantum Entanglement）It is a kind of quantum-mechanical phenomenon, theoretically defines, it is described For the special quantum state of a class of member's hybrid system with two or more, this quantum state can not be decomposed into member The tensor product of the respective quantum state of system（Tensor Product）.Generally, quantum entanglement is particle by two or two The molecular system of above grain, although particle may spatially be separated, but there is interactional phenomenon.
The field such as quantum-mechanical theory and quantum calculation is constantly developed, and is provided effectively for the development of modern information technologies Guarantee.Nineteen fifty-one, D.Bohm exists《Quantum theory》Middle re EPR thoughts, replace with two automatic rotary components original Coordinate and momentum, are further research, particularly experimental check is laid a good foundation.Nineteen fifty-two, D.Bohm exists《Physics is commented on》 On continuously deliver two articles, it is proposed that quantum-mechanical hidden variable is explained.2000, NBS was in ion trap system The Entangled State of four ions is realized on system.2005, NBS and Innsbruck ,Austria group announced respectively Realize the Entangled State of six and eight ions.In December, 2016, Pan Jianwei team of China Science ＆ Technology University by two kinds not Same method is prepared for the optimal entangled photons source of combination property, successfully realizes " ten photon entanglements " first, has refreshed photon and entangled Twine the world record of state preparation.On June 15th, 2017, famous magazine《Science》In the form of front cover paper, it was recently reported that China's " ink Son number " quantum satellite realizes the message of thousands of kilometers of quantum entanglements, the highest quantum transmission distance compared to 144 kilometers before this first It is current to have striden forward a crucial step across quantum communications are meaned on practical road from record.
Quantum entanglement is the scientific basic of the researchs such as Quantum Teleportation, quantum-key distribution, quantum calculation.However, all The influence of many practical factors, for example：Influenceed by experiment condition limitation and inevitable ambient noise, what is prepared tangles State is all not maximal entangled state.Information distortion will be caused by carrying out quantum communications and quantum calculation using this Entangled State.Cause This, improves actual Quantum Entangled States to being important research problem during quantum information is studied close to pure Entangled State.
The application of quantum entanglement includes：Quantum communication is applied to quantum state Teleportation.Quantum entanglement can realize quantum Secure communication, reaches current safe information transmission safest in theory.Quantum calculation is applied to quantum computer, but needs Solve following subject matter：Quantum algorithm, quantum coding, the physics system for realizing quantum calculation etc..
With the breakthrough achievement obtained in recent years in quantum research field, the research of quantum computer also further develops. R.Feynman encounters the problem of calculating data volume becomes abnormal huge in the research for simulating quantum appearance；Then, use is produced Quantized system constitutes computer to simulate the thought of quantum appearance, then operation time can reduce a lot.
20th century the eighties, the research of quantum computer predominantly stays in theoretical research stage.Until 20th century 90 Age, the P.Shor of AT＆T Labs proves that quantum calculation function completes logarithm operation and quantum prime factorization algorithm, and is somebody's turn to do Algorithm constitutes a serious threat to widely used RSA cryptographic algorithms, accelerates the development process of quantum computer.
2009, first of world programmable universal quantum computer is formal to be born in the U.S..Study quantum computer Purpose not replaces existing computer with it.Crucial the problem of is experimentally to realize that the manipulation to Micro quantum attitude is certain It is too difficult.Computer code is that computer realizes control and the basis calculated, and various information are represented as in computer-internal Binary form.At present, also there is certain limitation in the extensive realization and use of quantum computer, and quantum calculation is ground Study carefully, including the research of quantum algorithm and quantum coding, there is also many restrictions.But, with quantum theory and technology not Disconnected development, market potential is huge.
The content of the invention
(1) technical problem to be solved
Due to the limitation of practical factor, the problems such as distortion occurs in the measurement of quantum information, in order to which quantum information is better achieved Measurement, the purpose of the present invention is to propose to a kind of computer coding method based on quantum entanglement and least square method, and meter The exchange of information is completed in the information transfer that calculation machine is realized, has used quantum entanglement to realize the volume of binary information 0 and 1 Code, can be in one-to-one measurement and correction judgement with completing information in one-to-many communication.
(2) technical scheme
In order to solve the above-mentioned technical problem, the invention provides a kind of computer code based on quantum entanglement and least square method Method for transmitting information, including：
Part1, the information of transmission is converted into the computer code form based on quantum entanglement；
The information for having been converted to the computer code form based on quantum entanglement is transmitted by Part2, transmitting terminal；
Part3, receiving terminal are measured and decoded according to constraints, then after the information that transmitting terminal transmission comes is received Judge the correctness of each information.
Constraints is the basis that the computer code based on quantum entanglement and least square method realizes communication, is transmitting terminal With receiving terminal be required in accordance with rule.The constraints that computer code based on quantum entanglement and least square method is used It is described as follows.
Constraints Condition (1)：The mathematical description form of Quantum Entangled States is
|φ> = ε|0> + μ|1>
Wherein, | 0>With | 1>Represent quantum bit two kinds of possible states, measurement quantum bit 0 probability be | ε |2, measurement amount The probability of sub- bit 1 is | μ |2, and in the ideal case, meet | ε |2 + |μ|2 = 1。
Constraints Condition (2)：In actual measurement, due to being influenceed by physical condition, definition
| |ε|2 + |μ|2 – 1| <= df
Wherein, df is the error of given measurement.When the error of actually measurement is less than or equal to df, the numerical value of definition measurement is to connect It is near correct, meet the condition of Quantum Entangled States；Otherwise, the numerical value of definition measurement is inaccurate, is unsatisfactory for Quantum Entangled States Condition.
Constraints Condition (3)：Definition is apart from D.Binary coding (p1, p2 ..., pi ..., pn)2 In, p1 is designated as positioned at primary binary digit, little-endian is designated as pi (i=1,2 ...) successively, and last position is designated as pn.The numerical value apart from D that the numerical value apart from D for defining p1 is 1, p2 is 2；The like, the pi numerical value apart from D is i, finally The one pn numerical value apart from D is n.
In ideal conditions, the numerical value apart from D is positive integer.But, in actual measurement, apart from D measurement Numerical value is real number.
Constraints Condition (4)：Sign function Sgn (value) is defined as
When numerical value value is less than 0, sign function Sgn (value) return value is 0.
When numerical value value is more than 0, sign function Sgn (value) return value is 1.
Constraints Condition (5)：Each position adjacent thereto of computer code based on quantum entanglement can all be produced Raw quantum entanglement, adjacent information bit is in Entangled State：
|φ> = dp|0> + dq|1>
Wherein, the probability of measurement quantum bit 0 is | dp |2, the probability for measuring quantum bit 1 is | dq |2, and in ideal situation Under, meet | dp |2 + |dq|2 = 1。
Constraints Condition (6)：The hypothesis testing number of computer code based on quantum entanglement and least square method Be described as follows
Receive H0：|ts – td| < C
Refuse H0：|ts – td| >= C
Wherein, ts is the probability of ideally measured value, and td is the probability of the measured value under physical condition, and C is error The probability of critical value.
Constraints Condition (7)：In least square method, it is assumed that the observed value of measurement be (x1, y1), (x2, y2), …, (xn, yn)。
The best fit function of least square method is defined as
y = k*x
Wherein, y and x are real number, and k is set as constant.There is any two point real d1 and d2, N1 and N2 is integer:
(A) assume to meet N1<= d1<D2, then in least square method, determines that d1 and N1 meets best fit condition.If The value for determining d1 is N1;
(B) assume to meet d1< d2 <=N2, then in least square method, determines that d2 and N2 meets best fit condition.If The value for determining d2 is N2.
In Part1, the step of converting the information into the computer code form based on quantum entanglement includes：
Transmitting terminal determines the numerical value apart from D before transmission information.In binary coding（p1, p2, …, pi, …, pn）In, It is in primary binary digit and is designated as p1, the numerical value apart from D for defining p1 is 1, the numerical value apart from D for defining p2 is 2, successively Analogize, the numerical value apart from D for defining pi is i.
Each binary bit of information is represented as Quantum Entangled States form
|φ> = α|0> + β|1>
α and β is correspondence | 0>With | 1>The measurement probability of quantum bit.
Transmitting terminal needs each in coding being converted into following form before transmission information
Sgn(val)
When the binary digit is 0, val=- D (α2, β2);
When the binary digit is 1, val=D (α2, β2)。
Adjacent binary bit of information (pi, pj)2It is in Quantum Entangled States, Quantum Entangled States form
|φ> = dp|0> + dq|1>
Dp and dq is correspondence | 0>With | 1>The measurement probability of quantum bit.
Each information bit sent has unified form
Sgn (sign bit D (α2, β2)), (dp2, dq2)
In Part2, the information for having been converted to the computer code form based on quantum entanglement is transmitted by transmitting terminal, bag Include：
Transmitting terminal is transmitted using one-to-one or one-to-many form as needed:
Wherein, man-to-man transmission process is that transmitting terminal A sends information to receiving terminal B;
One-to-many transmission process is that transmitting terminal S sends information to receiving terminal Cs (c1, c2 ..., ci ..., cn), wherein, Each ci is the receiving terminal of equity.
Transmission process is performed parallel, and the transmission of each information bit is separate.
In Part3, receiving terminal is after the information that transmitting terminal transmission comes is obtained, and receiving terminal enters row information according to constraints Reception and measurement, and decoded, then judge the correctness of each information.
Receiving terminal is according to Sgn (sign bit D (α2, β2)), (dp2, dq2) reception of beacons and metrical information.
Receiving terminal measures α and β numerical value, in actual measurement, according to | | α |2 + |β|2 – 1| <=df constraint Whether the condition Verification binary bit of information meets the condition of Entangled State, to judge whether the measured value of the binary bit of information is accurate Really.
When the binary bit of information is unsatisfactory for the condition of Entangled State, the computer based on quantum entanglement and least square method The hypothesis testing checking α of coding：
Receive H0：|ts_α – td_α| < C_α
Refuse H0：|ts_α – td_α| >= C_α
Wherein, ts_ α is ideally measure α probability, and td_ α is measure α probability under physical condition, and C_ α are α mistake The probability of poor critical value.
β is verified in hypothesis testing：
Receive H0：|ts_β – td_β| < C_β
Refuse H0：|ts_β – td_β| >= C_β
Wherein, ts_ β is ideally measure β probability, and td_ β is measure β probability under physical condition, and C_ β are β mistake The probability of poor critical value.
When the binary bit of information is unsatisfactory for the condition of Entangled State, if it is assumed that examining checking α and β, wherein α and β have One is correct, that is, receives H0, and the measurement result of another exceeded error threshold value probability be it is incorrect, i.e., Refuse H0, illustrate the corresponding probability of the quantum bit of the binary digit is influenceed to occur in that mistake by practical factor, in weak Tangle state.
When the binary bit of information is unsatisfactory for the condition of Entangled State, if it is assumed that examining checking α and β either of which It is incorrect, that is, refuses H0, illustrates that the quantum bit of the binary digit is influenceed by practical factor and relieved Entangled State.
Constraints of the receiving terminal according to least square method, measurement distance D.
Receiving terminal is decoded according to Sgn (sign bit D) to the binary bit of information.
When measurement, which obtains numerical value value, is less than 0, sign function Sgn (value) return value is 0, the binary message Place value is 0.
When measurement, which obtains numerical value value, is more than 0, sign function Sgn (value) return value is 1, the binary message Place value is 1.
Receiving terminal measures dp and dq numerical value, in actual measurement, according to | | dp |2 + |dq|2 – 1| <=df's Constraints verifies whether adjacent information bit meets the condition of Entangled State.
In adjacent binary bit of information (pi, pj)2In, when binary bit of information pi is unsatisfactory for the condition of Entangled State, The hypothesis testing checking dp of computer code based on quantum entanglement and least square method：
Receive H0：|ts_dp – td_dp| < C_dp
Refuse H0：|ts_dp – td_dp| >= C_dp
Dq is verified in hypothesis testing：
Receive H0：|ts_dq – td_dq| < C_dq
Refuse H0：|ts_dq – td_dq| >= C_dq
Wherein, ts_dp and ts_dq is ideally measures dp and dq probability, and td_dp and td_dq are under physical condition Measure dp and dq probability, C_dp and C_dq for dp and dq error threshold value probability.
When binary bit of information pi is unsatisfactory for the condition of Entangled State, if it is assumed that examine checking dp and dq, wherein dp and It is correct that dq, which has one, that is, receives H0, and the probability that the measurement result of another has exceeded error threshold value is incorrect , that is, refuse H0, illustrate the corresponding probability of binary bit of information pi quantum bit is influenceed to occur in that mistake by practical factor By mistake, state is tangled in weak.
When binary bit of information pi is unsatisfactory for the condition of Entangled State, if it is assumed that examining any one of checking dp and dq All it is incorrect, that is, refuses H0, illustrates that binary bit of information pi quantum bit is influenceed to have relieved by practical factor and entangle Twine state.
Measuring method to binary bit of information pj measuring method binary bit of information pi adjacent thereto is identical.
After receiving terminal is measured, decoded information returns to binary coding (p1, p2 ..., pi ..., pn)2。
(3) beneficial effect
The beneficial effects of the invention are as follows can pass through a kind of computer coding method based on quantum entanglement and least square method Information transfer effectively enters row information exchange, meets accuracy requirement in a kind of message transmitting procedure based on quantum calculation, It can effectively overcome due to measurement error caused by the fragility of quantum and the limitation of physical condition, and show amount in actual measurement Son tangles state.
Brief description of the drawings
Fig. 1 is the flow chart of the computer coding method based on quantum entanglement and least square method.
Embodiment
Embodiments of the present invention are described in further detail with example below in conjunction with the accompanying drawings.Following instance is used to illustrate The present invention, but can not be used for limiting the scope of invention.
The physics that A.Einstein proposes one " perverse " in nineteen thirty-five is contemplated.In his imagination, two grains Son is reversely flown away from, and eventually arrives at the remote two ends of galaxy.Assuming that the two particles are in " tangling " state all the time, that is, Say, they are " telekineasis " in the sense that quantum mechanics, a particle can sense that its twin brothers are sent out immediately All raw, then when measuring a particle, another particle is also influenceed by this measurement behavior at once, as this is to twin Raw son can pass through space, and mystically to carry out instantaneous communication the same.
For A.Einstein imagination, people have carried out the experiment of light quantum：Photon signal is sent by an optical fiber, A pair of photons of one end are reacted at once by laser active, the photon of the other end.There is no an exchange of energy, however particle still with Certain mode shares information, and no space time theory can explain how this nonlocality produces.
When studying quantized system, each quantized system has a related wave function.Each quantum can only use it Various probability represented to describe, rather than with any definite numeral.Probability is determined by wave function completely.Particle is in specific bit Put wave function of the probability of appearance with the particle on the position relevant.Although, in theory can be with classical physics Absolutely determine measurement, the position of one moving object of judgement and prophesy and speed.And in the microcosmic particle world, it is impossible to it is pre- The motion of object is sayed, any one prophesy is all the prophesy on statistical significance in essence.Therefore, quantum theory is inherently Say it is probabilistic.
The invention provides a kind of information transferring method of the computer code based on quantum entanglement and least square method, its It can be divided into：Transmitting terminal is encoded according to quantum entanglement to the binary message for needing to transmit, and transmitting terminal is used as needed One-to-one, one-to-many form is transmitted, and receiving terminal is measured and decoded according to constraints, realizes that information bit is correct Judge.
Transmitting terminal to implement step as follows.
Transmitting terminal determines the numerical value apart from D before transmission information, and each binary bit of information is represented as quantum entanglement State form：|φ> = α|0> +β|1>, coding Sgn (sign bit D (α are carried out according to the value 0 and 1 of binary digit2, β2))。
Adjacent binary bit of information is represented as Quantum Entangled States form：|φ> = dp|0> + dq|1>.
Transmitting terminal completes computer code, and each binary message has following form
Sgn (sign bit D (α2, β2)), (dp2, dq2)
Transmission process is performed parallel, and the transmission of each information bit is separate.
Receiving terminal to implement step as follows.
Receiving terminal is after the information that transmitting terminal transmission comes is obtained, and receiving terminal enters the reception and survey of row information according to constraints Amount, and decoded, then judge the correctness of each information.
Receiving terminal is according to Sgn (sign bit D (α2, β2)), (dp2, dq2) reception of beacons and metrical information.
Receiving terminal measures α and β numerical value, according to | | α |2 + |β|2 – 1| <=df constraints verifies the binary system Whether information bit meets the condition of Entangled State, to judge whether the measured value of the binary bit of information is correct.When binary system letter When breath position is unsatisfactory for the condition of Entangled State, hypothesis testing is carried out, judgement has still relieved Entangled State in weak state of tangling.
Constraints of the receiving terminal according to least square method, measurement distance D.
Receiving terminal is decoded according to Sgn (sign bit D) to the binary bit of information, determines the binary message place value For 0 or 1.
Receiving terminal measures dp and dq numerical value, according to | | dp |2 + |dq|2 – 1| <=df constraints checking is adjacent Information bit whether meet the condition of Entangled State.When binary bit of information is unsatisfactory for the condition of Entangled State, hypothesis testing is carried out, Judge that adjacent information bit has still relieved Entangled State in weak state of tangling.
Successfully decoded, obtains transmission information.
Example 1：Realize the transmission of transmitting terminal A to receiving terminal B binary message 0110.
From, it is known that the information that transmitting terminal is sent to receiving terminal is (0110)2, transmitting terminal setpoint distance D, in binary coding
(p1, p2, p3, p4)2
It is p1 positioned at the binary digit of the 1st, little-endian is designated as p2 and p3 respectively, and last position is p4, i.e. n=4.If The numerical value apart from D that the numerical value apart from D for determining p1 is 1, p2 is 2, by that analogy.
Numerical value apart from D is designated as D1=1, D2=2, D3=3 and D4= 4。
Constraints Condition (7) least square method is set as y=k*x, k=1, i.e. y=x.Least square method is true Position of the binary message in its coding is determined.
Sender needs each in coding being converted into following form before transmission information：
Sgn (sign bit D (α2, β2)), (dp2, dq2)
When binary bit of information is 0, the val for defining Sgn (val) is negative；When binary bit of information is 1, Sgn is defined (val) val is positive number.Each binary bit of information is represented as Quantum Entangled States form：|φ> = α|0> +β|1>, The probability α and β that setting quantum entanglement is embodied are α respectively2=0.1 and β2=0.9。
Adjacent binary bit of information is represented as Quantum Entangled States form：|φ> = dp|0> + dq|1>.Set dp2 =0.2, dq2 = 0.8。
By Given information (0110)2Understand, each information is encoded to { Sgn (sign bit D (α by transmitting terminal A2, β2)), (dp2, dq2), it is specific as follows shown：
p1={-1(0.1, 0.9), (0.2, 0.8)}
p2={ 2(0.1, 0.9), (0.2, 0.8)}
p3={ 3(0.1, 0.9), (0.2, 0.8)}
p4={-4(0.1, 0.9), (0.2, 0.8)}
Receiving terminal B in the state of transmission conditions are preferable, that is, measured value in correct error range when, pass through above-mentioned volume Code and the constraints measurement observed are as follows：
Sign function Sgn (val) is defined as：When numerical value val is less than 0,0 is returned；When numerical value val is more than 0,1 is returned.
Receiving terminal receives p1={ -1 (0.1,0.9), (0.2,0.8) }.
Measurement is obtained apart from D=1, and according to least square method y=x, the position is first, and Sgn (val) is negative, by | | α |2 + |β|2 – 1| <=df=0.1, is obtained | 0.1+0.9-1 |=0<Df=0.1, α and β meets and tangles condition, by | | dp |2 + | dq|2 – 1| <=df, is obtained, | 0.2+0.8-1 |=0<Df, meets with adjacent bit and tangles condition.
So, the place value is 0 after p1 decodings.
Receiving terminal receives p2={ 2 (0.1,0.9), (0.2,0.8) }.
Measurement is obtained apart from D=2, according to least square method y=x, and the position is second, and Sgn (val) is positive number, and α and β are full Foot tangles condition, is met with adjacent bit and tangles condition.
So, the place value is 1 after p2 decodings.
The like.
Receiving terminal receives p3={ 3 (0.1,0.9), (0.2,0.8) }.
Measurement is obtained apart from D=3, and according to least square method y=x, the position is the 3rd, and Sgn (val) is positive number, and α and β are full Foot tangles condition, is met with adjacent bit and tangles condition.
So, the place value is 1 after p3 decodings.
Receiving terminal receives p4={ -4 (0.1,0.9), (0.2,0.8) }.
Measurement is obtained apart from D=4, and according to least square method y=x, the position is the 4th, and Sgn (val) is negative, and α and β are full Foot tangles condition, is met with adjacent bit and tangles condition.
So, the place value is 0 after p4 decodings.
The information received is decoded as 0110, the correct transmission of information is completed.
Example 2：Realize transmitting terminal S to the transmission of receiving terminal Cs_1 and Cs_2 binary message 0110.
From, it is known that the information that transmitting terminal is sent to receiving terminal is (0110)2。
Constraints Condition (7) least square method is set as y=k*x, k=1, i.e. y=x.
By Given information (0110)2, each information is encoded to { Sgn (sign bit D (α by transmitting terminal S2, β2)), (dp2, dq2), it is specific as follows shown：
p1={-1(0.1, 0.9), (0.2, 0.8)}
p2={ 2(0.1, 0.9), (0.2, 0.8)}
p3={ 3(0.1, 0.9), (0.2, 0.8)}
p4={-4(0.1, 0.9), (0.2, 0.8)}
Assuming that the information that receiving terminal Cs_1 is received is
p1={-1.2(0.1, 0.9), (0.2, 0.8)}
p2={ 2.25(0.1, 0.9), (0.2, 0.8)}
p3={ 3(0.1, 0.9), (0.2, 0.8)}
p4={-4(0.1, 0.9), (0.2, 0.8)}
By the receiving terminal Cs_1 numerical value D apart from D1=1.2 and D2=2.25, i.e., ranging offset value in this case is larger, actual Situation is D1=1 and D2=2。
N1 is met according to constraints Condition (7) (A)<= d1<D2, then in fitting, determines d1 and N1 Meet best fit condition.D1 value is set as N1.Obtained by p1, N1=1< d1=1.2 <D2=2.25, according to least square Method, obtains D1=1。
Obtained by p2, N1=2 are met according to constraints Condition (7) (A)< D2=2.25, obtain D2=2。
Assuming that the information that receiving terminal Cs_2 is received is
p1={-1.3(0.1, 0.9), (0.2, 0.8)}
p2={2.2(0.1, 0.9), (0.2, 0.8)}
p3={ 2.25(0.1, 0.9), (0.2, 0.8)}
p4={-4(0.1, 0.9), (0.2, 0.8)}
Assumed to meet N1 according to constraints Condition (7) (A)<= d1<D2, then in least square method, determines d1 Best fit condition is met with N1.D1 value is set as N1.
Obtained by p2, N1=2<= d1=2.2 < d2=2.25.Therefore, D is set2=2。
Assumed to meet d1 according to constraints Condition (7) (B)< d2 <=N2, then in least square method, Determine that d2 and N2 meets best fit condition.D2 value is set as N2.
Obtained by p3, d1=2.2< d2=2.25 <= N2=3.Therefore, set：D3=3。
According to constraints Condition (7) (A) and (B), obtained in receiving terminal Cs_1 and receiving terminal Cs_2 decodable codes Information：0110.
Example 3：Judge quantum entanglement state according to hypothesis testing.
It is assumed that transmitting terminal sends information 0110 to receiving terminal, the information that receiving terminal is measured is as follows：
p1={-1.1(0.1, 0.9), (0.9, 0.1)}
pi ={ 2.2(0.1, 0.9), (0.9, 0.1)}
pj ={ 2.25(0.1, 0.9), (0.5, 0.11)}
p4={ -4(0.1, 0.9), (0.9, 0.1)}
Set D2It is pi distance, D3It is pj distance.
In least square method, it can be drawn by pi and pj distance values, pi and pj is adjacent bit.
According to constraints Condition (5), each adjacent bit with it of the computer code based on quantum entanglement Quantum entanglement will be produced, adjacent binary bit of information is in Entangled State：|φ>=dp|0> + dq|1>.
Constraints Condition (2), in actual measurement, due to being influenceed by physical condition, definition
||ε|2 + |μ|2 – 1| <= df=0.1。
Measure pi adjacency information position (dp2, dq2) meet quantum entanglement relation.
The pj adjacent bit condition of tangling is：
|0.5+0.11–1|=0.39 > df =0.1。
When measuring pj with adjacent information bit, (dp2, dq2) quantum entanglement relation is unsatisfactory for, therefore, judge pj survey Value is affected, and is changed.
According to constraints Condition (6), when binary bit of information pj is unsatisfactory for the condition of Entangled State, based on amount Son tangles hypothesis testing the checking dp, setting C_dq=C_dp=0.1, Sqrt () with the computer code of least square method It is extraction of square root function.
Receive H0：|ts_dp – td_dp| < C_dp
Refuse H0：|ts_dp – td_dp| >= C_dp
Obtained by known pj, | ts_dp=Sqrt (0.9)-td_dp=Sqrt (0.5) |=0.24> C_dp =0.1.
Therefore, H0 is refused.
Dq is verified in hypothesis testing
Receive H0：|ts_dq – td_dq| < C_dq
Refuse H0：|ts_dq – td_dq| >= C_dq
Obtained by known pj, | ts_dq=Sqrt (0.1)-td_dq=Sqrt (0.11) |=0.015< C_dq = 0.1。
Therefore, illustrate that binary bit of information pj tangles state with juxtaposition in weak.
Finally it should be noted that：The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although The present invention is described in detail with reference to the foregoing embodiments, it will be understood by those within the art that：It still may be used To be modified to the technical scheme described in foregoing embodiments, or equivalent substitution is carried out to which part technical characteristic； And these modification or replace, do not make appropriate technical solution essence depart from various embodiments of the present invention technical scheme spirit and Scope.

Claims (1)

1. a kind of computer coding method based on quantum entanglement and least square method, it is characterised in that including：
Part1, the information of transmission is converted into the computer code form based on quantum entanglement；
The information for having been converted to the computer code form based on quantum entanglement is transmitted by Part2, transmitting terminal；
Part3, receiving terminal is measured and decoded according to constraints, then after the information that transmitting terminal transmission comes is received Judge the correctness of each information；
Constraints is the basis that computer code based on quantum entanglement and least square method realizes communication, is transmitting terminal and connects Receiving end be required in accordance with rule；
The constraints that computer code based on quantum entanglement and least square method is used is described as follows；
Constraints Condition (1)：The mathematical description form of Quantum Entangled States is
|φ> = ε|0> + μ|1>
Wherein, | 0>With | 1>Represent quantum bit two kinds of possible states, measurement quantum bit 0 probability be | ε |2, measure quantum The probability of bit 1 is | μ |2, and in the ideal case, meet | ε |2 + |μ|2 = 1；
Constraints Condition (2)：In actual measurement, due to being influenceed by physical condition, definition
| |ε|2 + |μ|2 – 1| <= df
Wherein, df is given measurement error；When the error of actually measurement is less than or equal to df, the numerical value of definition measurement is close Correctly, the condition of Quantum Entangled States is met；Otherwise, the numerical value of definition measurement is inaccurate, is unsatisfactory for Quantum Entangled States Condition；
Constraints Condition (3)：Definition is apart from D；Binary coding (p1, p2 ..., pi ..., pn)2In, position P1 is designated as in primary binary digit, little-endian is designated as pi (i=1,2 ...) successively, and last position is designated as pn；It is fixed The numerical value apart from D that the adopted p1 numerical value apart from D is 1, p2 is 2；The like, the pi numerical value apart from D is i, last position The pn numerical value apart from D is n；
In ideal conditions, the numerical value apart from D is positive integer；But, in actual measurement, apart from D measured value For real number；
Constraints Condition (4)：Sign function Sgn (value) is defined as
When numerical value value is less than 0, sign function Sgn (value) return value is 0；
When numerical value value is more than 0, sign function Sgn (value) return value is 1；
Constraints Condition (5)：Each position adjacent thereto of computer code based on quantum entanglement all can yield Son is tangled, and adjacent information bit is in Entangled State
|φ> = dp|0> + dq|1>
Wherein, the probability of measurement quantum bit 0 is | dp |2, the probability for measuring quantum bit 1 is | dq |2, and in the ideal case, Meet | dp |2 + |dq|2 = 1；
Constraints Condition (6)：The hypothesis testing mathematics of computer code based on quantum entanglement and least square method is retouched State as follows
Receive H0：|ts – td| < C
Refuse H0：|ts – td| >= C
Wherein, ts is the probability of ideally measured value, and td is the probability of the measured value under physical condition, and C is error The probability of critical value；
Constraints Condition (7)：In least square method, it is assumed that the observed value of measurement be (x1, y1), (x2, y2), …, (xn, yn)；
The best fit function of least square method is defined as
y = k*x
Wherein, y and x are real number, and k is set as constant；There is any two point real d1 and d2, N1 and N2 is integer；
(A) assume to meet N1<= d1<D2, then in least square method, determines that d1 and N1 meets best fit condition；If The value for determining d1 is N1；
(B) assume to meet d1< d2 <=N2, then in least square method, determines that d2 and N2 meets best fit condition；If The value for determining d2 is N2；
In Part1, the step of converting the information into the computer code form based on quantum entanglement includes：
Transmitting terminal determines the numerical value apart from D before transmission information, in binary coding (p1, p2 ..., pi ..., pn), P1 is designated as positioned at primary binary digit, the numerical value apart from D for defining p1 is 1, the numerical value apart from D for defining p2 is 2, successively Analogize, the numerical value apart from D for defining pi is i；
Each binary bit of information is represented as Quantum Entangled States form
|φ> = α|0> + β|1>
α and β is correspondence | 0>With | 1>The measurement probability of quantum bit；
Transmitting terminal needs each in coding being converted into following form before transmission information
Sgn(val)
When the binary digit is 0, val=- D (α2, β2)；
When the binary digit is 1, val=D (α2, β2)；
Adjacent binary bit of information (pi, pj)2It is in Quantum Entangled States, Quantum Entangled States form
|φ> = dp|0> + dq|1>
Dp and dq is correspondence | 0>With | 1>The measurement probability of quantum bit；
Each information bit sent has unified form
Sgn (sign bit D (α2, β2)), (dp2, dq2)
In Part2, the information for having been converted to the computer code form based on quantum entanglement is transmitted by transmitting terminal, bag Include：
Transmitting terminal uses one-to-one as needed, and one-to-many form is transmitted；
Wherein, man-to-man transmission process is that transmitting terminal A sends information to receiving terminal B；
One-to-many transmission process is that transmitting terminal S sends information to receiving terminal Cs (c1, c2 ..., ci ..., cn), wherein, Each ci is the receiving terminal of equity；
Transmission process is performed parallel, and the transmission of each information bit is separate；
In Part3, receiving terminal is after the information that transmitting terminal transmission comes is obtained, and receiving terminal enters connecing for row information according to constraints Receive and measure, and decoded, then judge the correctness of each information；
Receiving terminal is according to Sgn (sign bit D (α2, β2)), (dp2, dq2) reception of beacons and metrical information；
Receiving terminal measures α and β numerical value, in actual measurement, according to | | α |2 + |β|2 – 1| <=df constraints is tested The condition whether binary bit of information meets Entangled State is demonstrate,proved, to judge whether the measured value of the binary bit of information is accurate；
When the binary bit of information is unsatisfactory for the condition of Entangled State, the computer code based on quantum entanglement and least square method Hypothesis testing checking α：
Receive H0：|ts_α – td_α| < C_α
Refuse H0：|ts_α – td_α| >= C_α
Wherein, ts_ α is ideally measure α probability, and td_ α is measure α probability under physical condition, and C_ α are α mistake The probability of poor critical value；
β is verified in hypothesis testing：
Receive H0：|ts_β – td_β| < C_β
Refuse H0：|ts_β – td_β| >= C_β
Wherein, ts_ β is ideally measure β probability, and td_ β is measure β probability under physical condition, and C_ β are β mistake The probability of poor critical value；
When the binary bit of information is unsatisfactory for the condition of Entangled State, if it is assumed that examining checking α and β, wherein α and β to have one It is correct, that is, receives H0, and the probability that the measurement result of another has exceeded error threshold value is incorrect, that is, is refused H0, illustrate the corresponding probability of the quantum bit of the binary digit is influenceed to occur in that mistake by practical factor, is tangled in weak State；
When the binary bit of information is unsatisfactory for the condition of Entangled State, if it is assumed that the either of which for examining checking α and β is not Correctly, that is, refuse H0, illustrate that the quantum bit of the binary digit is influenceed by practical factor and relieved Entangled State；
Constraints of the receiving terminal according to least square method, measurement distance D；
Receiving terminal is decoded according to Sgn (sign bit D) to the binary bit of information；
When measurement, which obtains numerical value value, is less than 0, sign function Sgn (value) return value is 0, the binary message place value For 0；
When measurement, which obtains numerical value value, is more than 0, sign function Sgn (value) return value is 1, the binary message place value For 1；
Receiving terminal measures dp and dq numerical value, in actual measurement, according to | | dp |2 + |dq|2 – 1| <=df constraint bar Part verifies whether adjacent information bit meets the condition of Entangled State；
In adjacent binary bit of information (pi, pj)2In, when binary bit of information pi is unsatisfactory for the condition of Entangled State, it is based on The hypothesis testing checking dp of the computer code of quantum entanglement and least square method：
Receive H0：|ts_dp – td_dp| < C_dp
Refuse H0：|ts_dp – td_dp| >= C_dp
Dq is verified in hypothesis testing：
Receive H0：|ts_dq – td_dq| < C_dq
Refuse H0：|ts_dq – td_dq| >= C_dq
Wherein, ts_dp and ts_dq is ideally measures dp and dq probability, and td_dp and td_dq are under physical condition Measure dp and dq probability, C_dp and C_dq for dp and dq error threshold value probability；
When binary bit of information pi is unsatisfactory for the condition of Entangled State, if it is assumed that examining checking dp and dq, wherein dp and dq have One is correct, that is, receives H0, and the measurement result of another exceeded error threshold value probability be it is incorrect, i.e., Refuse H0, illustrate that the corresponding probability of binary bit of information pi quantum bit is influenceed by practical factor and occur in that mistake, locate State is tangled in weak；
When binary bit of information pi is unsatisfactory for the condition of Entangled State, if it is assumed that examining checking dp and dq either of which is It is incorrect, that is, refuse H0, illustrate that binary bit of information pi quantum bit is influenceed by practical factor and relieved Entangled State；
Measuring method to binary bit of information pj measuring method binary bit of information pi adjacent thereto is identical；
After receiving terminal is measured, decoded information returns to binary coding (p1, p2 ..., pi ..., pn)2。
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