Randomness evaluation method for continuous variable source independent quantum random number generator under limited sampling bandwidth condition

Abstract

The invention belongs to the technical field of quantum information communication, and discloses a randomness evaluation method of a continuous variable source independent quantum random number generator under a limited sampling bandwidth condition, which comprises the following steps: setting a sampling interval of an analog-to-digital converter and carrying out oversampling in each pulse period, calculating the ratio of the maximum sampling peak voltage to the pulse peak voltage; calculating the total variance of the corrected measurement signal noise; calculating the measurement precision of the corrected orthogonal component; calculating the lower bound of the corrected quantum condition minimum entropy; and the generation rate of the random number is calculated. According to the method, the influence of the limited sampling bandwidth of the analog-to-digital converter on the variance of the measurement signal is considered, and the evaluation formula of the quantum condition minimum entropy is corrected, so that the random number content which can be extracted from the measurement result can be correctly estimated, and the actual safety of the continuous variable source-independent quantum random number generator is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of quantum information communication and relates to a randomness evaluation method for a continuous variable source-independent quantum random number generator under limited sampling bandwidth conditions. Background Art

[0002] With the accelerated development of information technology, the status of random numbers in information security, numerical simulation, confidential communication and other fields is becoming increasingly important. Quantum random number generators prepare random numbers by collecting quantum random processes. Quantum random processes meet the uncertainty principle of quantum mechanics and can ensure the true randomness of the random numbers they generate. They have received extensive attention and research. In the research of quantum random number generators, continuous variable source-independent quantum random number generators can eliminate the problem of untrusted random sources, relax the assumptions about quantum entropy sources, and have a relatively simple structure and a high random number generation rate, becoming the mainstream solution.

[0003] Continuous variable source-independent quantum random number generators can be divided into two schemes: based on homodyne detection and based on heterodyne detection. The continuous variable source-independent quantum random number generator based on heterodyne detection uses two balanced zero-beat detectors and does not require random modulation of the phase modulator, but the structure is relatively complex. The continuous variable source-independent quantum random number generator based on homodyne detection uses a balanced zero-beat detector, and most protocols require an additional phase modulator to modulate the phase of the local oscillator light. Later, the researchers proposed a continuous variable source-independent quantum random number generator based on homodyne detection that does not require an additional phase modulator. The continuous variable source-independent quantum random number generator based on phase randomized local oscillator light drives the laser with a pulse voltage, and the local oscillator light pulses it emits have a random phase, so that no additional phase modulator is required, further simplifying the system structure.

[0004] Although the theoretical security of the continuous variable source-independent quantum random number generator based on phase randomized local oscillator light has been fully demonstrated, the impact of the imperfection of actual devices on the actual security of the system has been ignored. The electrical signal output by the balanced homodyne detector will be discretely sampled by the analog-to-digital converter. In previous security analyses, it is usually assumed that the sampling bandwidth of the analog-to-digital converter is infinite. However, in actual systems, the sampling bandwidth of the analog-to-digital converter is always limited, which may affect parameter estimation, thereby causing incorrect estimation of the extractable random number content, threatening actual security. Summary of the invention

[0005] The present invention aims at the technical problem that the existing continuous variable source-independent quantum random number generator based on phase randomized local oscillator light does not consider the influence of limited sampling bandwidth on related parameters and thus threatens the security during security analysis. The present invention provides a randomness evaluation method for a continuous variable source-independent quantum random number generator under limited sampling bandwidth conditions, considers the influence of the limited sampling bandwidth of an analog-to-digital converter on the variance of the measurement signal, and corrects the evaluation formula of the quantum conditional minimum entropy, so that the random number content that can be extracted from the measurement result can be correctly estimated, thereby improving the actual security of the continuous variable source-independent quantum random number generator.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The present invention provides a randomness evaluation method for a continuous variable source-independent quantum random number generator under a limited sampling bandwidth condition, comprising the following steps:

[0008] 1) Set the sampling interval of the analog-to-digital converter and perform oversampling in each pulse cycle. Only the peak voltage is sampled for each pulse signal, and the ratio of the maximum sampled peak voltage to the pulse peak voltage is calculated;

[0009] 2) Calculate the total variance of the corrected measurement signal noise based on the ratio of the maximum sampling value point to the pulse peak value point;

[0010] 3) Calculate the measurement accuracy of the corrected orthogonal component using the total variance of the corrected measurement signal noise;

[0011] 4) Using the measurement accuracy of the modified orthogonal components, calculate the lower bound of the modified quantum conditional minimum entropy;

[0012] 5) Using the lower bound of the modified quantum conditional minimum entropy, calculate the random number generation rate.

[0013] In the above technical solution, the calculation formula of the total variance of the corrected measurement signal noise is as follows:

[0014]

[0015] in: is the measurement variance of pure vacuum noise, is the classic electrical noise measurement variance, k is the maximum sampling value voltage U m And the pulse peak voltage U p ratio, G is the gain of the differential amplifier, |β| 2 is the number of photons contained in the local oscillator light pulse.

[0016] In the above technical solution, the calculation formula of the measurement accuracy of the corrected orthogonal component is as follows:

[0017]

[0018] Where: ADC is the sampling resolution, f rep is the pulse repetition frequency, f samp is the sampling bandwidth of the analog-to-digital converter.

[0019] In the above technical solution, the calculation formula of the lower bound of the quantum conditional minimum entropy is as follows:

[0020]

[0021] In the above technical solution, the calculation formula of the random number generation rate is as follows:

[0022] R(Q δ |E)=H min (Q δ |E)f rep .

[0023] Compared with the prior art, the present invention has the following beneficial effects:

[0024] The present invention takes into account the influence of the limited sampling bandwidth of the analog-to-digital converter on the total variance of the measurement signal noise, and further modifies the evaluation formula of the quantum conditional minimum entropy, so that the random number content that can be extracted from the measurement result can be correctly estimated, and the actual security of the continuous variable source-independent quantum random number generator is improved. Based on this, the present invention finds that the random number generation rate does not increase with the increase of the pulse repetition frequency, and with the goal of maximizing the quantum random number generation rate, a method for optimizing the pulse repetition frequency is given, which can further improve the random number generation rate and the performance of the quantum random number generator. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Schematic diagram of the experimental setup of a continuous variable source-independent quantum random number generator based on phase randomized local oscillator light.

[0026] Figure 2 The effect of different sampling bandwidths on quantum conditional minimum entropy estimation.

[0027] Figure 3 This is the relationship between the pulse repetition frequency and the quantum random number generation rate under different sampling bandwidth conditions. DETAILED DESCRIPTION

[0028] The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention. Unless otherwise specified, the technical means used in the examples are conventional means known to those skilled in the art. The test methods in the following examples are conventional methods unless otherwise specified.

[0029] Embodiment 1

[0030] like Figure 1 The schematic diagram of the experimental setup of the continuous variable source-independent quantum random number generator based on phase randomized local oscillator light is shown. The local oscillator light emitted by the gain-switched laser passes through a beam splitter with a splitting ratio of 1:99, and 1% of the local oscillator light is measured by an optical power meter to monitor the local oscillator light power; 99% of the local oscillator light is input into a 50:50 beam splitter, and after interference coupling with the unknown quantum signal input from the other port of the beam splitter, it is measured by a balanced zero-difference detector composed of two detectors and a differential amplifier, and the output electrical signal is sampled by an analog-to-digital converter. The sampling range of the analog-to-digital converter is expressed as [-N+δ ADC / 2,N-3δ ADC / 2],N=3σ t , the sampling precision is n, then the sampling resolution is δ ADC =N / 2 n-1 .

[0031] Gaussian distribution, then the quantum conditional minimum entropy H min (Q δ |E)Satisfy:

[0032]

[0033] Among them: δ is the measurement accuracy, and E represents the eavesdropper's side information.

[0034] Then, based on formula (1), in order to accurately estimate the lower bound of the extractable randomness, it is necessary to estimate the measurement accuracy δ through a calibration procedure.

[0035] During the calibration process, the signal port is blocked to input a pure vacuum signal, and the optical power P of the local oscillator light is changed. LO , we can get the total variance of the corresponding measurement signal noise as follows:

[0036]

[0037] in: is the measurement variance of pure vacuum noise, is the variance of the classic electrical noise measurement.

[0038] The input LO light is treated as a classical field, and the LO light annihilation operator β represents the local oscillator light amplitude, |β| 2 represents the number of photons contained in the local oscillator light pulse, θ i represents the phase of the local oscillator light, and the annihilation operator of the input signal-vacuum state is

[0039] The two detectors of the balanced homodyne detector convert photons into electrons. After the two photocurrent signals are subtracted, they pass through a differential amplifier with a gain of G to output an electrical pulse signal. The pulse peak voltage is as follows:

[0040]

[0041] From formula (3), we can see that the orthogonal component value of the input signal is With the pulse voltage peak U p Linearly proportional.

[0042] According to formula (3), when the variance of the orthogonal components of the vacuum state is When , the measured variance of pure vacuum noise is as follows:

[0043]

[0044] Then the optical power of the local oscillator light P LO and the photon number |β| 2 The relationship can be expressed as follows:

[0045]

[0046] Where: h is Planck's constant, v is the central wavelength of the local oscillator light, and t0 is the duration of the local oscillator light pulse.

[0047] According to formulas (4) and (5), it can be concluded that the measurement variance of pure vacuum noise is The optical power P of the local oscillator light LO When the input signal is in a vacuum state, the total variance of the signal noise will be measured The formula (2) is transformed as follows:

[0048]

[0049] in: a g =G 2 t0 / 2hv.

[0050] Therefore, according to the local oscillator light power P LO and the measured signal noise variance The data can be fitted to a calibration straight line, and the intercept c of the calibration straight line is the classic electrical noise measurement variance. Slope a g It can be used to calculate the variance of vacuum fluctuation noise, and the local oscillator light power P LO Measured using an optical power meter, the corresponding measurement accuracy can be expressed as follows:

[0051]

[0052] The electrical signal output by the balanced homodyne detector is sampled by an analog-to-digital converter. In the past, it was usually assumed that the analog-to-digital converter can always sample the peak value of the output voltage pulse signal. However, since the sampling bandwidth of the actual analog-to-digital converter is limited, the sampled value often deviates from the peak value of the pulse signal.

[0053] In order to ensure that the pulse peak value can be sampled correctly, the analog-to-digital converter generally performs oversampling, that is, a large number of samples are taken in each pulse cycle, and each sampling time interval is t s =1 / f samp , where f samp It is the sampling bandwidth of the analog-to-digital converter. Once the sampling position of a pulse peak is determined, downsampling can be performed according to the signal repetition frequency, and only the peak point of each pulse signal is sampled.

[0054] Assuming that the duration of the light pulse is much shorter than the response time of the homodyne detector, the normal component of the input signal is linearly proportional to the peak value of the output voltage pulse signal. If the voltage signal waveform output by the homodyne detector is Gaussian and satisfies

[0055]

[0056] Among them: U p is the pulse peak voltage, μ and σ are the mean and standard deviation of the pulse.

[0057] For simplicity, we choose μ = w0 / 2, σ 2 =(w0 / 8) 2 , w0 is the pulse width. Pulse repetition period t0 = 1 / f rep The relationship between the pulse width w0 and R duty =w0 / t0, where: f rep is the pulse repetition frequency, R duty is the duty cycle of the pulse.

[0058] The present invention takes into account that the sampling of the analog-to-digital converter is always limited and cannot accurately sample the peak voltage, and thus derives the maximum sampling peak voltage U m And the pulse peak voltage U p There is a sampling bias, which is expressed as follows:

[0059]

[0060] When Δt=-t s / 2(t s / 2), the sampling deviation ΔU reaches the maximum value, that is:

[0061]

[0062] Then the maximum sampling peak voltage U m And the pulse peak voltage U p The ratio k is:

[0063]

[0064] It can be seen that the ratio k is determined by the sampling bandwidth and the pulse repetition frequency. The larger the k, the smaller the sampling value deviation ΔU. Therefore, due to the limited sampling bandwidth of the analog-to-digital converter, the signal variance measured during the calibration process will change, and the total variance of the corrected measurement signal noise will be as follows:

[0065]

[0066] Then the measurement accuracy δ of the corrected orthogonal component is as follows:

[0067]

[0068] Then the modified quantum conditional minimum entropy H min (Q δ |E) can be expressed as follows:

[0069]

[0070] Based on the above formula, the modified random number generation rate is as follows:

[0071] R(Q δ |E)=H min (Q δ |E)f rep (14)

[0072] According to formula (14), the pulse repetition frequency f rep , get the maximum random number generation rate.

[0073] In a specific embodiment, assuming that the central wavelength v of the gain-switched laser is 1550 nm, R duty =50%, |β| 2 =5×10 8 , N=10, n=8.

[0074] Figure 2 is the pulse repetition frequency f rep=50MHz, the influence of different sampling bandwidths on the estimation of quantum conditional minimum entropy. The red dashed line in the figure represents the value of quantum conditional minimum entropy estimated under the condition of considering the influence of limited sampling bandwidth, and the black solid line represents the value of quantum conditional minimum entropy estimated under the condition of not considering the influence of sampling bandwidth under ideal conditions. It can be clearly seen that for a fixed pulse repetition frequency, as the sampling bandwidth increases, the estimated quantum conditional minimum entropy is closer to the ideal value. In other words, if the influence of limited sampling bandwidth is not considered, it will cause the quantum conditional minimum entropy H min (Q δ |E) is overestimated, affecting the security of the output quantum random numbers.

[0075] Figure 3 The relationship between the pulse repetition frequency and the quantum conditional minimum entropy under different sampling bandwidth conditions. It can be seen that under the same sampling bandwidth conditions, as the pulse repetition frequency increases, the value of the quantum random number generation rate first increases and then decreases, and does not increase infinitely with the increase of the pulse repetition frequency. Therefore, under the condition of a fixed sampling bandwidth, the pulse repetition frequency has a maximum value. According to the optimization method given, an optimal pulse repetition frequency f can be obtained. rep .

[0076] Therefore, the present invention takes into account the influence of the limited sampling bandwidth of the analog-to-digital converter on the total variance of the measurement signal noise, and further modifies the evaluation formula of the quantum conditional minimum entropy, so that the random number content that can be extracted from the measurement result can be correctly estimated, and the actual security of the continuous variable source-independent quantum random number generator is improved. Based on this, it is found that the random number generation rate does not increase with the increase of the pulse repetition frequency, and with the goal of maximizing the quantum random number generation rate, a method for optimizing the pulse repetition frequency is given, which can further improve the random number generation rate and the performance of the quantum random number generator.

[0077] The embodiments described above are only preferred embodiments of the present invention and are only used to explain the present invention, not to limit the scope of implementation of the present invention. For those skilled in the art, other implementation methods can certainly be easily made by replacement or modification based on the technical contents disclosed in this specification. Therefore, all changes and improvements made on the principles of the present invention should be included in the scope of the patent application of the present invention.

Claims

1. A randomness evaluation method for a continuous variable source-independent quantum random number generator under finite sampling bandwidth conditions, characterized in that: The following steps are involved: 1) Set the sampling interval of the analog-to-digital converter and perform oversampling in each pulse cycle. Only the peak voltage is sampled for each pulse signal, and the ratio of the maximum sampled peak voltage to the pulse peak voltage is calculated; 2) Calculate the total variance of the corrected measurement signal noise based on the ratio of the maximum sampling value point to the pulse peak value point; 3) Calculate the measurement accuracy of the corrected orthogonal component using the total variance of the corrected measurement signal noise; 4) Using the measurement accuracy of the modified orthogonal components, calculate the lower bound of the modified quantum conditional minimum entropy; 5) Using the lower bound of the modified quantum conditional minimum entropy, calculate the random number generation rate.

2. The randomness evaluation method according to claim 1, characterized in that: The calculation formula of the total variance of the modified measurement signal noise is as follows: in: is the measurement variance of pure vacuum noise, is the classic electrical noise measurement variance, k is the maximum sampling value voltage U m And the pulse peak voltage U p ratio, G is the gain of the differential amplifier, |β| 2 is the number of photons contained in the local oscillator light pulse.

3. The randomness evaluation method according to claim 2, characterized in that: The calculation formula of the measurement accuracy of the modified orthogonal component is as follows: Where: ADC is the sampling resolution, f rep is the pulse repetition frequency, f samp is the sampling bandwidth of the analog-to-digital converter.

4. The randomness evaluation method according to claim 3, characterized in that: The calculation formula for the lower bound of the quantum conditional minimum entropy is as follows:

5. The randomness evaluation method according to claim 4, characterized in that: The calculation formula for the random number generation rate is as follows: R(Q δ |E)=H min (Q δ |E)f rep 。

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