CN114285568B - Key rate acquisition method and system for double-scanning 4-intensity MDI-QKD system - Google Patents
Key rate acquisition method and system for double-scanning 4-intensity MDI-QKD system Download PDFInfo
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Abstract
The invention provides a key rate acquisition method and a system of a double-scanning 4-intensity MDI-QKD system, which acquire an expression of a third scanning parameter according to a first scanning parameter and a second scanning parameter; determining an upper limit of the third scanning parameter according to the expression of the third scanning parameter, the upper limit of the first scanning parameter and the lower limit of the second scanning parameter, and determining a lower limit of the third scanning parameter according to the expression of the third scanning parameter, the lower limit of the first scanning parameter and the upper limit of the second scanning parameter; determining a scanning range according to the lower limit of the third scanning parameter and the upper limit of the third scanning parameter; calculating the key rate according to a third scanning parameter in the scanning range, and taking the minimum value of all the key rates as the final key rate; the invention integrates the first scanning parameter and the second scanning parameter into one parameter, and can realize the calculation of the key rate by only scanning the one parameter, thereby greatly reducing the calculated amount and improving the calculation efficiency.
Description
Technical Field
The invention relates to the technical field of quantum secret communication, in particular to a key rate acquisition method and system of a double-scanning 4-intensity MDI-QKD system.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The measuring device independent quantum key distribution (MDI-QKD) system can defend side channel attacks of any detection end, and is easy to combine with a decoy state method, thereby having wide development prospect. However, in practical applications, the key rate decreases rapidly with distance due to the finite code length effect of the spoofed MDI-QKD system.
In recent years, many studies have been focused on improving the key rate and code distance of the system, and have achieved considerable results. In order to increase the key rate of the system, many improvements have been proposed, such as global optimization method, joint constraint method, 4-intensity decoy method, double scan 4-intensity decoy method, etc. The effect of these improved methods is evaluated at present, mainly by respectively calculating the key rate size and distribution optimized over the whole communication distance of QKD when using the improved method and other methods under certain QKD device conditions, and then comparing and judging the merits of the improved method. Among the above-mentioned improved methods, the 4-strength decoy method is a mainstream method because it can promote the key rate by several orders of magnitude, and after the use of the double-scan 4-strength decoy, the key rate can be further improved. For a dual scan 4 intensity MDI-QKD system, the architecture is shown in fig. 1, consisting of three parts Alice, bob and Charlie, where Alice and Bob are the sender of the quantum state preparation, with a completely uniform structure, while pulsing to a third party Charlie. Charlie is used as a measuring party for Bell state measurement of the received pulse pairs, and Charlie can also be an untrusted eavesdropper (Eve).
The inventors have found that in QKD systems, there are mainly two scenarios involving key rate computation: the first scenario is that during the QKD system operation, the key rate needs to be calculated, providing basis for some parameter settings in post-processing. And in the second scenario, parameter optimization is required to be performed on the QKD system, for example, when the working environment of the QKD system changes or is compared with other protocol methods, the key rate is required to be repeatedly subjected to analog calculation under a certain QKD equipment condition until an optimal system parameter point is obtained. For the dual scan method, it is required to be respectively in the intervalsAnd->Scanning step by step and calculatingCalculated +.>The minimum value is taken as the final key rate, and the calculation mode is obviously more complex than the traditional calculation mode. Let +.>The upper part needs to scan h points, and the interval is +.>The m points need to be scanned, then a total of scans are neededThe h×m points are traced and calculated to obtain the final key rate R. For the second scene, under the general condition, the existing calculation requirements h and m are more than or equal to 100, and the final key rate R under a group of system parameters can be obtained at least by scanning and calculating 10000 times; secondly, repeated iteration is needed until the optimal system parameters are found, and the iteration times are more than or equal to 5000 times under the general condition; finally we also need to calculate the final key rate R under the optimized system parameters at each communication distance, 200 times assuming a communication distance range of 0-200km,1km, one acquisition point. The whole process in total requires at least the calculation of 100×100×5000×200=10 10 This is clearly a huge calculation for a conventional computer, which is about 30 hours, which obviously seriously affects the calculation efficiency of the key rate.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a key rate acquisition method and a system for a double-scanning 4-intensity MDI-QKD system, which are used for acquiring parameters(i.e. the first scan parameter) and +.>The second scanning parameters are integrated into one parameter, and the calculation of the key rate can be realized by only scanning the one parameter, so that the calculation amount is greatly reduced, and the calculation efficiency is improved.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the first aspect of the invention provides a key rate acquisition method for a dual scan 4 intensity MDI-QKD system.
A key rate acquisition method for a dual scan 4 intensity MDI-QKD system, comprising the steps of:
obtaining an expression of a third scanning parameter according to the first scanning parameter and the second scanning parameter;
determining an upper limit of the third scanning parameter according to the expression of the third scanning parameter, the upper limit of the first scanning parameter and the lower limit of the second scanning parameter, and determining a lower limit of the third scanning parameter according to the expression of the third scanning parameter, the lower limit of the first scanning parameter and the upper limit of the second scanning parameter;
determining a scanning range according to the lower limit of the third scanning parameter and the upper limit of the third scanning parameter;
and calculating the key rate according to a third scanning parameter in the scanning range, and taking the minimum value of all the key rates as the final key rate.
Further, the upper limit of the third scan parameter is: a difference between the upper limit of the first scan parameter and the lower limit of the second scan parameter of 0.5 times;
the lower limit of the third scan parameter is: the difference between the lower limit of the first scan parameter and the upper limit of the second scan parameter is 0.5 times.
Further, the lower limit of the scanning range is equal to or smaller than the lower limit of the third scanning parameter, and the upper limit of the scanning range is equal to or larger than the upper limit of the third scanning parameter.
Further, the upper limit and the lower limit of the first scanning parameter and the upper limit and the lower limit of the second scanning parameter are obtained through a combined constraint method and a Chernov boundary.
Further, according to the third scanning parameter, an expected value upper limit of the phase inversion error rate and an expected value lower limit of the single photon counting rate are obtained, and the key rate is calculated according to the expected value upper limit of the phase inversion error rate and the expected value lower limit of the single photon counting rate.
Further, for a certain third scanning parameter in the scanning range, when the third scanning parameter is determined and the second scanning parameter is the maximum value, the minimum key rate under the third scanning parameter is obtained.
Further, the upper limit of the expected value of the phase inversion error rate is a function of the third scanning parameter, and the lower limit of the expected value of the single photon counting rate is a function of the third scanning parameter and the second scanning parameter;
and when the third scanning parameter is determined, obtaining the functional relation between the maximum value of the second scanning parameter and the third scanning parameter according to a linear equation programming method.
A second aspect of the invention provides a key rate acquisition system for a dual scan 4 intensity MDI-QKD system.
A key rate acquisition system for a dual scan 4 intensity MDI-QKD system, comprising:
a parameter conversion module configured to: obtaining an expression of a third scanning parameter according to the first scanning parameter and the second scanning parameter;
an upper and lower limit determination module configured to: determining an upper limit of the third scanning parameter according to the expression of the third scanning parameter, the upper limit of the first scanning parameter and the lower limit of the second scanning parameter, and determining a lower limit of the third scanning parameter according to the expression of the third scanning parameter, the lower limit of the first scanning parameter and the upper limit of the second scanning parameter; the method comprises the steps of carrying out a first treatment on the surface of the
A scan range determination module configured to: determining a scanning range according to the lower limit of the third scanning parameter and the upper limit of the third scanning parameter;
a key rate calculation module configured to: and calculating the key rate according to a third scanning parameter in the scanning range, and taking the minimum value of all the key rates as the final key rate.
A third aspect of the invention provides a computer readable storage medium having stored thereon a program which when executed by a processor performs the steps in a key rate acquisition method of a dual scan 4 intensity MDI-QKD system according to the first aspect of the invention.
A fourth aspect of the invention provides an electronic device comprising a memory, a processor and a program stored on the memory and executable on the processor, the processor implementing the steps in a key rate acquisition method of a dual scan 4 intensity MDI-QKD system according to the first aspect of the invention when the program is executed.
Compared with the prior art, the invention has the beneficial effects that:
the key rate obtaining method and system of the double-scanning 4-intensity MDI-QKD system of the invention can obtain two parameters of scanningAnd->The method integrates a parameter, only one parameter is required to be scanned, and the calculated amount is greatly reduced on the premise of unchanged calculation precision; for the first scene, the key rate calculation rate can be improved by more than 100 times; for the second scene, the time can be shortened to tens of minutes from the original 30 hours, and the scientific research efficiency of researchers is greatly improved.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a block diagram of a dual scan 4 intensity MDI-QKD system provided in the background of the invention.
Fig. 2 is a flow chart of the dual scan 4 intensity MDI-QKD system operation provided in example 1 of the present invention.
Fig. 3 is a flow chart of a key rate obtaining method of a dual scan 4 intensity MDI-QKD system according to embodiment 1 of the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples.
It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
Embodiments of the invention and features of the embodiments may be combined with each other without conflict.
Example 1:
for a dual scan 4 intensity MDI-QKD system, the workflow is shown in fig. 2, specifically as follows:
s1: alice and Bob modulate and transmit N light pulses respectively, and the light pulses at both ends are probability-based respectivelyAnd->(wherein l A L=o, x, y, z represents the quantum state selected by Alice, r B R=o, x, y, z represents Bob's selected quantum state) is randomly modulated into 4 different quantum states: respectively being Alice terminal vacuum state o A (Bob terminal o) B ) First decoy state X under X-basis vector A (Bob terminal x) B ) And a second decoy state y A (Bob terminal y) B ) Signal state Z under Z-basis vector A (Bob terminal z) B ) The four intensities are respectively +.> And->(Bob terminal> And->)。
S2: charlie performs Bell state measurement on quantum states sent by Alice and Bob, and publishes measurement results to Alice and Bob after N times of measurement are completed.
S3: alice and Bob retain the data under the measurement of the valid response and discard the other data.
S4: alice and Bob perform base vector comparison on the data, retain the data corresponding to the Z base vector selected by both sides, obtain a string of bits for generating an original key, and use the rest of data for decoy state estimation.
S5: alice and Bob post-process the bit string, including single photon counting rate estimation, phase inversion error rate estimation, error correction, double scanning, secret amplification and other processes to obtain the final key.
The key rate can be expressed as:
the meaning of the formula is to use a double scanning method in an intervalAnd->Scanning onWill->As final key rate, wherein +.>Representation->(i.e. the first scan parameter) and +.>The key rate at (i.e., the second scan parameter) can be expressed as:
wherein,and->Indicating that Alice and Bob send l respectively A And r B The probability of n as the photon number in the quantum state; e (E) zz ＝T zz /S zz Indicating bit flip error rate of effective detection event in zz state sent by Alice and Bob; h (x) = -xlog 2 (x)-(1-x)log 2 (1-x) represents shannon entropy; f is error correction efficiency; epsilon cor Indicating failure probability of error correction; epsilon PA Failure probability of privacy amplification; ε' and ∈>Coefficients when the smooth minimum entropy chain rule and the maximum entropy chain rule are used respectively; />Andthe lower limit of the single photon counting rate and the corresponding upper limit of the phase inversion error rate in the zz state can be respectively expressed as follows according to the Chernov boundary:
wherein O is L (Y)＝[1+δ′ 1 (Y)]Y and O U (Y)＝[1-δ′ 2 (Y)]Y is the lower limit and the upper limit of the actual observed value obtained according to the expected value Y respectively; n (N) zz The number of effective detection events when the zz state is sent to Alice and Bob;is the lower limit of the expected value of the single photon counting rate, < >>The upper limit of the bit-flipping error rate of the single photon under the Z-base vector is equal to the upper limit of the bit-flipping error rate of the single photon under the X-base vector in value<e 11 > U I.e. +.>Wherein-> Wherein the count rateCorresponding expected value->Error bit count rate +.>Corresponding expected value->n lr Representing the effective count for Alice and Bob using the lr state, m lr Error counts representing the corresponding states; lower and upper limits<S + > L And<S _ > U 、/>and->And->Can be obtained by combining constraint methods and the Chernofar boundary.
From the above, the calculation of scanning two parameters simultaneously is huge, but we find that the parameters can be usedAnd->The same calculation result can be achieved by integrating one parameter and only scanning the one parameter, so that the calculation amount is obviously greatly reduced.
Specifically, as shown in fig. 3, the embodiment provides a key rate obtaining method of a dual scan 4 intensity MDI-QKD system, which includes the following steps:
obtaining an expression of a third scanning parameter according to the first scanning parameter and the second scanning parameter;
determining an upper limit of the third scanning parameter according to the expression of the third scanning parameter, the upper limit of the first scanning parameter and the lower limit of the second scanning parameter, and determining a lower limit of the third scanning parameter according to the expression of the third scanning parameter, the lower limit of the first scanning parameter and the upper limit of the second scanning parameter;
determining a scanning range according to the lower limit of the third scanning parameter and the upper limit of the third scanning parameter;
and calculating the key rate according to a third scanning parameter in the scanning range, and taking the minimum value of all the key rates as the final key rate.
The key rate acquisition method comprises the following detailed procedures:
parameters of the orderThen t 11 (i.e. the third scan parameter) is +.>And->An important step is to reasonably determine t 11 One typical method is to determine the upper and lower limits using the following formulas:
it will be appreciated that the scan range may be [ T ] L ，T U ]I.e. the lower limit of the scanning range is T L The upper limit of the scanning range is T U In other embodiments, the lower limit of the scan range may be less than T L The upper limit of the scanning range may be greater than T U Those skilled in the art may perform the custom selection according to specific working conditions, which will not be described herein.
The lower limit of the expected value of the single photon count rate<s 11 > L And an upper limit on the expected value of the phase inversion bit error rateCan be rewritten as:
visible in the lightIs t 11 And->For each determined t 11 The values may have a series of linear sets +.>In the linear set, from the above +.>Lower limit of expected value of single photon count rate<s 11 > L And the upper limit of the expected value of the phase inversion error rate +.>As can be seen in the formula, when +.>Take the maximum value H (t) 11 ) Lower limit of expected value of single photon count rate<s 11 > L Is minimal, and is further->Is minimal.
Thus, at each determined t 11 In the value, the corresponding value is obtained by direct analysis and calculationIs the minimum value R (t) 11 ) Then scan t 11 And calculates a key rate R (t) 11 ) The minimum value is taken as the final key rate.
The key step is thatMaximum value H (t) 11 ) Is due to->t 11 Is->Andfor each determined t 11 The value, H (t) can be obtained by a linear equation programming method 11 ) In particular, the formula:
visible H (t) 11 ) Is t 11 Is a function of the single photon count rate, the lower limit of the expected value<s 11 > L The method can be written as follows:
obviously, it can be just in interval [ T L ,T U ]Scanning up and calculating the key rate R (t 11 ) The minimum key rate is obtained as the final key rate, namely:
it follows that by modifying the correlation of the parameters, the present embodiment changes scanning two parameters to scanning only one parameter, which will greatly reduce the calculation time of the key rate.
By adopting the optimization method, the key rate calculation rate can be improved by more than 100 times, the key rate calculation time for the second scene can be shortened to tens of minutes from the original 30 hours, and the scientific research efficiency of researchers is greatly improved.
Example 2:
embodiment 2 of the present invention provides a key rate acquisition system for a dual scan 4 intensity MDI-QKD system, comprising:
a parameter conversion module configured to: obtaining an expression of a third scanning parameter according to the first scanning parameter and the second scanning parameter;
an upper and lower limit determination module configured to: determining an upper limit of the third scanning parameter according to the expression of the third scanning parameter, the upper limit of the first scanning parameter and the lower limit of the second scanning parameter, and determining a lower limit of the third scanning parameter according to the expression of the third scanning parameter, the lower limit of the first scanning parameter and the upper limit of the second scanning parameter;
a scan range determination module configured to: determining a scanning range according to the lower limit of the third scanning parameter and the upper limit of the third scanning parameter;
a key rate calculation module configured to: and calculating the key rate according to a third scanning parameter in the scanning range, and taking the minimum value of all the key rates as the final key rate.
The operation method of the system is the same as the key rate obtaining method of the scan 4 intensity MDI-QKD system provided in embodiment 1, and will not be described here again.
Example 3:
embodiment 3 of the present invention provides a computer-readable storage medium having stored thereon a program which, when executed by a processor, implements the steps in a key rate acquisition method for a dual scan 4 intensity MDI-QKD system as described in embodiment 1 of the present invention.
Example 4:
embodiment 4 of the present invention provides an electronic device, including a memory, a processor, and a program stored on the memory and executable on the processor, where the processor executes the program to implement the steps in the key rate acquisition method of the dual scan 4 intensity MDI-QKD system according to embodiment 1 of the present invention.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, magnetic disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Those skilled in the art will appreciate that implementing all or part of the above-described methods in accordance with the embodiments may be accomplished by way of a computer program stored on a computer readable storage medium, which when executed may comprise the steps of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), or the like.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A key rate acquisition method of a double-scanning 4-intensity MDI-QKD system is characterized by comprising the following steps of:
the method comprises the following steps:
obtaining an expression of a third scanning parameter according to the first scanning parameter and the second scanning parameter;
determining an upper limit of the third scanning parameter according to the expression of the third scanning parameter, the upper limit of the first scanning parameter and the lower limit of the second scanning parameter, and determining a lower limit of the third scanning parameter according to the expression of the third scanning parameter, the lower limit of the first scanning parameter and the upper limit of the second scanning parameter; specifically, the upper limit of the third scan parameter is: a difference between the upper limit of the first scan parameter and the lower limit of the second scan parameter of 0.5 times; the lower limit of the third scan parameter is: a difference between a lower limit of the first scan parameter and an upper limit of the second scan parameter that is 0.5 times;
determining a scanning range according to the lower limit of the third scanning parameter and the upper limit of the third scanning parameter;
and calculating the key rate according to a third scanning parameter in the scanning range, taking the minimum value of all the key rates as the final key rate, specifically, obtaining an expected value upper limit of the phase inversion error rate and an expected value lower limit of the single photon counting rate according to the third scanning parameter, and calculating the key rate according to the expected value upper limit of the phase inversion error rate and the expected value lower limit of the single photon counting rate.
2. The key rate acquisition method of a dual scan 4 intensity MDI-QKD system of claim 1, wherein:
the lower limit of the scanning range is equal to or smaller than the lower limit of the third scanning parameter, and the upper limit of the scanning range is equal to or larger than the upper limit of the third scanning parameter.
3. The key rate acquisition method of a dual scan 4 intensity MDI-QKD system of claim 1, wherein:
the upper and lower limits of the first scan parameter and the upper and lower limits of the second scan parameter are obtained by a joint constraint method and a Chernofar boundary.
4. The key rate acquisition method of a dual scan 4 intensity MDI-QKD system of claim 1, wherein:
and for a certain third scanning parameter in the scanning range, when the third scanning parameter is determined and the second scanning parameter is the maximum value, obtaining the minimum key rate under the third scanning parameter.
5. The key rate acquisition method of a dual scan 4 intensity MDI-QKD system of claim 4, wherein:
the upper limit of the expected value of the phase inversion error rate is a function of the third scanning parameter, and the lower limit of the expected value of the single photon counting rate is a function of the third scanning parameter and the second scanning parameter;
and when the third scanning parameter is determined, obtaining the functional relation between the maximum value of the second scanning parameter and the third scanning parameter according to a linear equation programming method.
6. A key rate acquisition system for a dual scan 4 intensity MDI-QKD system, characterized by:
comprising the following steps:
a parameter conversion module configured to: obtaining an expression of a third scanning parameter according to the first scanning parameter and the second scanning parameter;
an upper and lower limit determination module configured to: determining an upper limit of the third scanning parameter according to the expression of the third scanning parameter, the upper limit of the first scanning parameter and the lower limit of the second scanning parameter, and determining a lower limit of the third scanning parameter according to the expression of the third scanning parameter, the lower limit of the first scanning parameter and the upper limit of the second scanning parameter; specifically, the upper limit of the third scan parameter is: a difference between the upper limit of the first scan parameter and the lower limit of the second scan parameter of 0.5 times; the lower limit of the third scan parameter is: a difference between a lower limit of the first scan parameter and an upper limit of the second scan parameter that is 0.5 times;
a scan range determination module configured to: determining a scanning range according to the lower limit of the third scanning parameter and the upper limit of the third scanning parameter;
a key rate calculation module configured to: and calculating the key rate according to a third scanning parameter in the scanning range, taking the minimum value of all the key rates as the final key rate, specifically, obtaining an expected value upper limit of the phase inversion error rate and an expected value lower limit of the single photon counting rate according to the third scanning parameter, and calculating the key rate according to the expected value upper limit of the phase inversion error rate and the expected value lower limit of the single photon counting rate.
7. A computer readable storage medium having stored thereon a program which when executed by a processor performs the steps in the key rate acquisition method of a dual scan 4 intensity MDI-QKD system as claimed in any one of claims 1 to 5.
8. An electronic device comprising a memory, a processor, and a program stored on the memory and executable on the processor, wherein the processor performs the steps in the key rate acquisition method of the dual scan 4 intensity MDI-QKD system of any of claims 1-5.
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