Phase Compensation Method for Continuous Variable System Based on Stokes Parameter Encoding

Abstract

The present invention discloses a phase compensation method for a continuous variable system based on Stokes parameter encoding. The process is as follows: calculate the Jones matrix of the encoded light beam at the entire transmitting end; calculate the theoretical output formulas of Stokes parameters S2 and S3; plot the theoretical S2 and S3 output curves; take the maximum values of the theoretical S2 and S3 output curves; plot the actual detected S2 and S3 output curves; take the maximum values of the actual detected S2 and S3 output curves; calculate the difference between the maximum actual value of S2 and the maximum theoretical value, calculate the difference between the maximum actual value of S3 and the maximum theoretical value, and the average value after the two differences is the compensation phase ψ; superimpose the compensation phase ψ into ψ2, that is, the phase of the entire continuous variable system based on Stokes parameter encoding is compensated. The above method solves the phase difference caused by the fast and slow axes of the optical fiber changing with the environment, and ensures the accuracy of Stokes parameter encoding.

Description

Technical Field

[0001] The present invention belongs to the technical field related to communication and quantum cryptography, and particularly relates to a phase compensation method for a continuous variable quantum key distribution system using Stokes parameter encoding. Background Art

[0002] Since 1984, quantum key distribution technology has been continuously developing. Quantum key distribution can provide theoretically secure keys for two locations.

[0003] Quantum key distribution is divided into two types: discrete variable and continuous variable. Among them, discrete variable has developed relatively fast, and its secure distance for generating keys is also increasing continuously; while continuous variable originally developed relatively slowly. However, since the continuous variable exceeded 80 kilometers in the 2013 paper, continuous variable has also developed rapidly. But currently, all are based on amplitude-phase modulation schemes, and all systems are also for fiber optic systems. A continuous variable quantum key distribution system based on the GG02 protocol has not been realized in free space, mainly because there is no good encoder.

[0004] However, for an encoder based on optical fiber, the polarization of the encoded light is elliptical polarization. The fast and slow axes of the optical fiber will cause phase differences due to environmental changes, resulting in continuous changes in the polarization state during encoding and transmission. To achieve correct encoding, it is necessary to solve the polarization state changes caused by the fast and slow axes of the optical fiber.

[0005] In the prior art, after searching, no technical solution has been found in publicly available journal literature regarding the "Stokes parameter encoder" that can well solve the polarization state changes caused by the fast and slow axes of the optical fiber, nor has it been found in relevant patent literature records; therefore, the prior art has not been able to well solve this problem. Summary of the Invention

[0006] The present invention provides a phase compensation method for a continuous variable system based on Stokes parameter encoding, aiming to solve the problem of polarization state changes caused by the fast and slow axes of the optical fiber and ensure the accuracy of Stokes parameter encoding.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] The phase compensation method for a continuous variable system based on Stokes parameter encoding of the present invention has the following process:

[0009] The first step: Calculate the Jones matrix of the encoded light beam at the entire transmitting end;

[0010] The second step: Calculate the theoretical output formulas of Stokes parameters S2 and S3;

[0011] The third step: Take ψ1 as a non-zero fixed value, and ψ2 traverses from 0 to 2π to plot the theoretical S2 and S3 output curves;

[0012] Step 4: Obtain the maximum values S2_THE_MAX and S3_THE_MAX of the theoretical S2 and S3 output curves;

[0013] Step 5: Take ψ1 as a fixed non-zero value, let ψ2 traverse from 0 to 2π, and plot the actual detected S2 and S3 output curves;

[0014] Step 6: Obtain the maximum values S2_ACT_MAX and S3_ACT_MAX of the actual detected S2 and S3 output curves;

[0015] Step 7: Calculate the difference between S2_ACT_MAX and S2_THE_MAX, calculate the difference between S3_ACT_MAX and S3_THE_MAX, and the average value after the two differences is the compensation phase ψ;

[0016] Step 8: Superimpose the compensation phase ψ into ψ2, that is, the phase of the entire continuous variable system based on Stokes parameter encoding is compensated.

[0017] Where the meanings of each symbol are:

[0018] S1: The difference in the number of photons between horizontally polarized light and vertically polarized light;

[0019] S2: The difference in the number of photons between +45-degree linearly polarized light and -45-degree linearly polarized light;

[0020] S3: The difference in the number of photons between left-handed circularly polarized light and right-handed circularly polarized light;

[0021] S2_THE_MAX: The phase coordinate value corresponding to the theoretical maximum value of the S2 curve;

[0022] S3_THE_MAX: The phase coordinate value corresponding to the theoretical maximum value of the S3 curve;

[0023] S2_ACT_MAX: The phase coordinate value corresponding to the actual maximum value of the S2 curve;

[0024] S3_ACT_MAX: The phase coordinate value corresponding to the actual maximum value of the S3 curve.

[0025] In the first step described above: The J of the Jones matrix Alice = J PBS * J PM2 * J FR * J PBS * J PM1 * J FR * J LD .

[0026] In the second step described above:

[0027] S2 = a H + *a V +a V + *a H ;

[0028] S3 = i(a V + *a H -a H + *a V );

[0029] Where:

[0030] a H —— Creation operator in the direction of the horizontal polarization component;

[0031] a H + —— Annihilation operator in the direction of the horizontal polarization component;

[0032] a V —— Creation operator in the direction of the vertical polarization component;

[0033] a V + —— Annihilation operator in the direction of the vertical polarization component;

[0034] i—— Imaginary unit, i 2 = -1;

[0035] Then, combining with the Jones matrix J of the encoded light beam at the entire transmitter end Alice it can be calculated that:

[0036] S2_THE = a LO *[sin(2θ)*sin(ψ1)*sin(ψ2) - sin(4θ)*cos(ψ2)*sin 2 (ψ

[0037] 1 / 2)];

[0038] S3_THE == a LO *[sin(2θ)*sin(ψ1)*cos(ψ2) - sin(4θ)*sin(ψ2)*sin 2 (ψ

[0039] 1 / 2)];

[0040] Where:

[0041] a LO —— Amplitude of the local oscillator light, light intensity coefficient, and the square is the light intensity of the local oscillator light;

[0042] θ —— The angle of rotation of the Faraday rotator;

[0043] ψ1 —— The phase angle loaded by the phase modulator PM1;

[0044] ψ2 —— The phase angle loaded by the phase modulator PM2.

[0045] In the third step described above, substituting ψ1 and ψ2 into S2_THE and S3_THE, two sine curves can be obtained, and the theoretical S2 and S3 output curves are plotted.

[0046] In the fifth step described above, after the values of ψ1 and ψ2 are taken, the entire continuous-variable quantum key distribution system is run, and the actual detected S2 and S3 output curves are plotted.

[0047] The encoder in the continuous-variable system described above includes a fiber optic phase modulator PM1 and a fiber optic phase modulator PM2; ψ1 is the phase loaded by the fiber optic phase modulator PM1; ψ2 is the phase loaded by PM2.

[0048] The S2 and S3 described above are Stokes parameter encoded signal lights, which obey two-dimensional Gaussian modulation.

[0049] The S2 is the difference in the number of photons between the +45-degree linearly polarized light and the -45-degree linearly polarized light; S3 is the difference in the number of photons between the left-handed circularly polarized light and the right-handed circularly polarized light.

[0050] The traversal of ψ2 from 0 to 2π means selecting the numerical values of 950 to 1050 evenly distributed points between 0 and 2π.

[0051] Adopting the above technical solution, the continuous-variable system phase compensation method of the present invention can solve the phase difference caused by the fast and slow axes of the optical fiber changing with the environment. By compensating this phase, the polarization state of the encoded elliptically polarized light after transmission through the fast and slow axes of the optical fiber can be made consistent with the loaded polarization state, ensuring the accuracy of Stokes parameter encoding. Brief Description of the Drawings

[0052] Figure 1 It is a schematic flow chart of the phase compensation method of the present invention. Detailed Embodiments

[0053] The following is a more detailed description of the specific embodiments of the present invention with reference to the accompanying drawings through the description of the embodiments, so as to help those skilled in the art have a more complete, accurate and in-depth understanding of the inventive concept and technical solution of the present invention.

[0054] Figure 1 Shown is a schematic flow chart of the phase compensation method of the continuous-variable system based on Stokes parameter encoding of the present invention.

[0055] In order to solve the problems existing in the prior art, overcome its defects, and achieve the invention purpose of solving the problem of polarization state change caused by the fast and slow axes of optical fibers and ensuring the accuracy of Stokes parameter encoding, the technical solution adopted by the present invention is as follows:

[0056] As Figure 1 shown, the phase compensation method for a continuous variable system based on Stokes parameter encoding of the present invention has the following process:

[0057] The first step: Calculate the Jones matrix of the encoded light beam at the entire transmitting end;

[0058] The second step: Calculate the theoretical output formulas of Stokes parameters S2 and S3;

[0059] The third step: Take ψ1 as a non-zero fixed value, and ψ2 traverses from 0 to 2π to plot the theoretical S2 and S3 output curves;

[0060] The fourth step: Take the maximum values S2_THE_MAX and S3_THE_MAX of the theoretical S2 and S3 output curves;

[0061] The fifth step: Take ψ1 as a non-zero fixed value, and ψ2 traverses from 0 to 2π to plot the actual detected S2 and S3 output curves;

[0062] The sixth step: Take the maximum values S2_ACT_MAX and S3_ACT_MAX of the actual detected S2 and S3 output curves;

[0063] The seventh step: Calculate the difference between S2_ACT_MAX and S2_THE_MAX, calculate the difference between S3_ACT_MAX and S3_THE_MAX, and the average value after the two differences is the compensation phase ψ;

[0064] The eighth step: Superimpose the compensation phase ψ into ψ2, that is, the phase of the entire continuous variable system based on Stokes parameter encoding is compensated.

[0065] The meanings of each symbol are as follows:

[0066] S1: The difference in the number of photons between horizontally polarized light and vertically polarized light;

[0067] S2: The difference in the number of photons between +45-degree linearly polarized light and -45-degree linearly polarized light;

[0068] S3: The difference in the number of photons between left-handed circularly polarized light and right-handed circularly polarized light;

[0069] S2_THE_MAX: The phase coordinate value corresponding to the theoretical maximum value of the S2 curve;

[0070] S3_THE_MAX: The phase coordinate value corresponding to the theoretical maximum value of the S3 curve;

[0071] S2_ACT_MAX: Obtain the phase coordinate value corresponding to the actual maximum value of the S2 curve;

[0072] S3_ACT_MAX: Obtain the phase coordinate value corresponding to the actual maximum value of the S3 curve.

[0073] The phase compensation method for a continuous variable system based on Stokes parameter encoding of the present invention can solve the phase difference caused by the fast and slow axes of the optical fiber changing with the environment. By compensating this phase, the polarization state of the encoded elliptically polarized light can be made consistent with the loaded polarization state after transmission through the fast and slow axes of the optical fiber, ensuring the accuracy of Stokes parameter encoding.

[0074] The encoder in the continuous variable system includes a fiber optic phase modulator PM1 and a fiber optic phase modulator PM2; ψ1 is the phase loaded by the fiber optic phase modulator PM1; ψ2 is the phase loaded by PM2.

[0075] The S2 and S3 mentioned above are Stokes parameter encoded signal lights, subject to two-dimensional Gaussian modulation.

[0076] The S2 is the difference in the number of photons between the +45-degree linearly polarized light and the -45-degree linearly polarized light; the S3 is the difference in the number of photons between the left-handed circularly polarized light and the right-handed circularly polarized light.

[0077] The traversal of ψ2 from 0 to 2π means selecting the numerical values of 950 to 1050 evenly distributed points between 0 and 2π.

[0078] Specifically, in the first step:

[0079] The J of the Jones matrix Alice = J PBS * J PM2 * J FR * J PBS * J PM1 * J FR * J LD .

[0080] In the formula:

[0081] J Alice ——The Jones matrix of the light emitted from the Alice side;

[0082] J PBS ——The Jones matrix of the PBS; PBS is a fiber optic polarization beam splitter;

[0083] J PM2 ——The Jones matrix of PM2; PM is a fiber optic phase modulator;

[0084] J FR—— Jones matrix of FR; FR is a fiber optic Faraday rotator;

[0085] J PM1 —— Jones matrix of PM1;

[0086] J LD —— Jones matrix of LD; LD is a laser.

[0087] In the second step described above,

[0088] S2 = a H + *a V +a V + *a H ;

[0089] S3 = i(a V + *a H -a H + *a V );

[0090] Where:

[0091] a H —— Creation operator in the direction of the horizontal polarization component;

[0092] a H + —— Annihilation operator in the direction of the horizontal polarization component;

[0093] a V —— Creation operator in the direction of the vertical polarization component;

[0094] a V + —— Annihilation operator in the direction of the vertical polarization component;

[0095] i—— Imaginary unit, i 2 = -1;

[0096] Then, combining the Jones matrix J of the encoded beam at the entire transmitter end Alice it can be calculated that:

[0097] S2_THE = a LO *[sin(2θ)*sin(ψ1)*sin(ψ2)-sin(4θ)*cos(ψ2)*sin 2 (ψ

[0098] 1 / 2)];

[0099] S3_THE == a LO*[sin(2θ)*sin(ψ1)*cos(ψ2)-sin(4θ)*sin(ψ2)*sin 2 (ψ

[0100] 1 / 2)]。

[0101] In the formula:

[0102] a LO —— Amplitude of local oscillator light, light intensity coefficient, and the square is the light intensity of local oscillator light;

[0103] θ —— Angle of rotation of the Faraday rotator;

[0104] ψ1 —— Phase angle loaded by phase modulator PM1;

[0105] ψ2 —— Phase angle loaded by phase modulator PM2.

[0106] Step 3: Take ψ1 as a non-zero fixed value, let ψ2 traverse from 0 to 2π, substitute them into S2_THE and S3_THE, two sine curves can be obtained, and draw the theoretical S2 and S3 output curves;

[0107] In the said Step 3, substitute ψ1 and ψ2 into S2_THE and S3_THE, two sine curves can be obtained, and draw the theoretical S2 and S3 output curves.

[0108] In the said Step 5, after the values of ψ1 and ψ2 are taken, run the entire continuous variable quantum key distribution system, and draw the actual detected S2 and S3 output curves.

[0109] The present invention has been described exemplarily above in conjunction with the accompanying drawings. Obviously, the specific implementation of the present invention is not limited by the above-mentioned manner. As long as various non-substantive improvements are made by adopting the method concept and technical solution of the present invention, or the concept and technical solution of the present invention are directly applied to other occasions without improvement, they are all within the protection scope of the present invention.

Claims

1. A phase compensation method for a continuous variable system based on Stokes parameter encoding, characterized in that: The process of the compensation method is as follows: The first step: Calculate the Jones matrix of the encoded light beam at the entire transmitting end; The second step: Calculate the theoretical output formulas of Stokes parameters S2 and S3; The third step: Take ψ1 as a fixed non-zero value, and ψ2 traverses from 0 to 2π, and plot the theoretical S2 and S3 output curves; The fourth step: Take the maximum values S2_THE_MAX and S3_THE_MAX of the theoretical S2 and S3 output curves; The fifth step: Take ψ1 as a fixed non-zero value, and ψ2 traverses from 0 to 2π, and plot the actual detected S2 and S3 output curves; The sixth step: Take the maximum values S2_ACT_MAX and S3_ACT_MAX of the actual detected S2 and S3 output curves; The seventh step: Calculate the difference between S2_ACT_MAX and S2_THE_MAX, calculate the difference between S3_ACT_MAX and S3_THE_MAX, and the average value after the two differences is the compensation phase ψ; The eighth step: Superimpose the compensation phase ψ into ψ2, that is, the phase of the entire continuous variable system based on Stokes parameter encoding is compensated; Where the meanings of each symbol are: S1: The difference in the number of photons between horizontally polarized light and vertically polarized light; S2: The difference in the number of photons between +45-degree linearly polarized light and -45-degree linearly polarized light; S3: The difference in the number of photons between left-handed circularly polarized light and right-handed circularly polarized light; S2_THE_MAX: The phase coordinate value corresponding to the theoretical maximum value of the S2 curve; S3_THE_MAX: The phase coordinate value corresponding to the theoretical maximum value of the S3 curve; S2_ACT_MAX: The phase coordinate value corresponding to the actual maximum value of the S2 curve; S3_ACT_MAX: The phase coordinate value corresponding to the actual maximum value of the S3 curve; In the encoder of the continuous variable system, it includes a fiber optic phase modulator PM1 and a fiber optic phase modulator PM2; ψ1 is the phase angle loaded by the fiber optic phase modulator PM1; ψ2 is the phase angle loaded by the fiber optic phase modulator PM2.

2. The phase compensation method for a continuous variable system based on Stokes parameter encoding according to claim 1, characterized in that: In the first step described above: J of the Jones matrix Alice = J PBS * J PM2 * J FR * J PBS * J PM1 * J FR * J LD ; In the formula: J Alice —— Jones matrix of the outgoing light from the Alice side; J PBS ——Jones matrix of PBS; PBS is a fiber optic polarization beam splitter; J PM2 ——Jones matrix of PM2; PM is fiber optic phase modulator; J FR —— Jones matrix of FR; FR is a fiber optic Faraday rotator; J PM1 —— Jones matrix of PM1; J LD ——Jones matrix of LD; LD is a laser.

3. The phase compensation method for a continuous variable system based on Stokes parameter encoding according to claim 2, characterized in that: In the second step, S2 = a H + *a V + a V + *a H ; S3 = i(a V + *a H −a H + *a V ); In the formula: a H —— Creation operator in the direction of the horizontal polarization component; a H + —— Annihilation operator in the direction of the horizontally polarized component; a V —— Creation operator in the direction of the vertically polarized component; a V + —— Annihilation operator in the direction of the vertically polarized component; i - the imaginary unit, i2 = -1; Then, combined with the Jones matrix J of the encoded beam at the entire transmitting end Alice it can be calculated that: S2_THE = a LO *[sin(2θ) * sin(ψ1) * sin(ψ2) - sin(4θ) * cos(ψ2) * sin 2 (ψ1 / 2)]; S3_THE==a LO *[sin(2θ)*sin(ψ1)*cos(ψ2) - sin(4θ)*sin(ψ2)*sin 2 (ψ1 / 2)]; In the formula: a LO —— The amplitude of the local oscillator light, the light intensity coefficient, and the square is the light intensity of the local oscillator light; θ - the angle of rotation of the Faraday rotator.

4. The phase compensation method for a continuous variable system based on Stokes parameter encoding according to claim 3, characterized in that: In the third step, substituting ψ1 and ψ2 into S2_THE and S3_THE, two sine curves can be obtained, and the theoretical S2 and S3 output curves are plotted.

5. The phase compensation method for a continuous variable system based on Stokes parameter encoding according to claim 1, characterized in that: In the fifth step, after the values of ψ1 and ψ2 are taken, the entire continuous variable quantum key distribution system is run, and the actual detected S2 and S3 output curves are plotted.

6. The phase compensation method for a continuous variable system based on Stokes parameter encoding according to claim 1, characterized in that: the S2 and S3 are Stokes parameter encoded signal lights, which obey two-dimensional Gaussian modulation.

7. The phase compensation method for a continuous variable system based on Stokes parameter encoding according to claim 1, characterized in that: the ψ2 traverses from 0 to 2π, which means selecting the numerical values of 950 to 1050 uniformly distributed points between 0 and 2π.

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