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Entropy

A Gaussian-Distributed Quantum Random Number Generator Using Vacuum Shot Noise

Min Huang, Ziyang Chen, Yichen Zhang, Hong Mei Guo

Published Jun 2, 2020• 18 citations
Publisher

Abstract

Among all the methods of extracting randomness, quantum random number generators are promising for their genuine randomness. However, existing quantum random number generator schemes aim at generating sequences with a uniform distribution, which may not meet the requirements of specific applications such as a continuous-variable quantum key distribution system. In this paper, we demonstrate a practical quantum random number generation scheme directly generating Gaussian distributed random sequences based on measuring vacuum shot noise. Particularly, the impact of the sampling device in the practical system is analyzed. Furthermore, a related post-processing method, which maintains the fine distribution and autocorrelation properties of raw data, is exploited to extend the precision of generated Gaussian distributed random numbers to over 20 bits, making the sequences possible to be utilized by the following system with requiring high precision numbers. Finally, the results of normality and randomness tests prove that the generated sequences satisfy Gaussian distribution and can pass the randomness testing well.

DOI
10.3390/e22060618

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Among all the methods of extracting randomness, quantum random number generators are promising for their genuine randomness. However, existing quantum random number generator schemes aim at generating sequences with a uniform distribution, which may not meet the requirements of specific applications such as a continuous-variable quantum key distribution system. In this paper, we demonstrate a practical quantum random number generation scheme directly generating Gaussian distributed random sequences based on measuring vacuum shot noise. Particularly, the impact of the sampling device in the practical system is analyzed. Furthermore, a related post-processing method, which maintains the fine distribution and autocorrelation properties of raw data, is exploited to extend the precision of generated Gaussian distributed random numbers to over 20 bits, making the sequences possible to be utilized by the following system with requiring high precision numbers. Finally, the results of normality and randomness tests prove that the generated sequences satisfy Gaussian distribution and can pass the randomness testing well.
Quantum random number generators represent one of the most promising techniques for producing truly and unique random numbers, essential in many applications such as quantum communication and cryptography protocols. In this work, we report an experimental implementation of vacuum-based quantum random number generator. By measuring the quantum fluctuations of the radiation ground state, a mixture of a perfectly Gaussian distributed random signal—originating from the intrinsic randomness in the quantum measurement— and an undesired classical electronic noise is obtained. Using an adequate post-processing, the undesired classical contribution of the electronic noise is removed to produce final, quasi-uniformly distributed random bit sequences. The high-quality character of the generated random bits is confirmed by applying the statistical tests of the NIST SP 800-22 test battery.
The shot noise of vacuum states is a kind of quantum noise and is totally random. In this paper a nondeterministic random number generation scheme based on measuring the shot noise of vacuum states is presented and experimentally demonstrated. We use a homodyne detector to measure the shot noise of vacuum states. Considering that the frequency bandwidth of our detector is limited, we derive the optimal sampling rate so that sampling points have the least correlation with each other. We also choose a method to extract random numbers from sampling values, and prove that the influence of classical noise can be avoided with this method so that the detector does not have to be shot-noise limited. The random numbers generated with this scheme have passed ent and diehard tests.
The Gaussian Error, represented by random numbers with a Gaussian distribution, plays a critical role in the security of modern lattice-based cryptography. Lattice-based cryptography is the most important category of post-quantum cryptography capable of resisting attacks from both classical and quantum.While current schemes of generating Gaussian Error used in lattice cryptography face severe challenges. On the one hand, the current scheme produces an approximate Gaussian distribution rather than the rigorously proven Gaussian distribution required in lattice cryptography, posing a security risk. Meanwhile, the Gaussian Error of current schemes is obtained by using algorithms to compute uniformly distributed random numbers, which lack provable randomness and also pose security risks. On the other hand, the generation rate of Gaussian Error is not high enough for many applications of cryptographic systems in current schemes. To address these challenges, this paper proposes a novel scheme that uses a quantum random number generator(QRNG) to generate the Gaussian Error, which follows a theoretically proven Gaussian distribution and satisfies rigorous security justification in lattice cryptography. Furthermore, based on the quantum mechanical process of measuring vacuum fluctuations and the principle of minimum entropy under classical noise conditions, the Gaussian Error obtained by our scheme is theoretically unpredictable, further enhancing the security of lattice cryptography compared to the current schemes. Finally, an experiment for generating Gaussian Error was constructed, and our experimental results demonstrate that the Gaussian Error generation rate is 1 G/s, which achieves higher speed among existing works.
Quantum random number generators (QRNGs) are currently in high demand across a large number of cryptographic applications as secure sources of true randomness. In this work, we characterize the conditions from which randomness can be extracted in a QRNG based on homodyne measurements of vacuum fluctuations by assessing the impact of experimental limitations, such as the digitizer resolution or the presence of excess local oscillator (LO) noise due to an unbalanced detection. Moreover, we propose an estimation method to quantify the excess entropy contribution introduced by an unbalanced detection and analyze the implementation of the post-processing algorithm. Finally, we submitted the generated numbers to a set of statistical tests to assess the quality of its output randomness and verified that it passes the standard libraries.
Quantum random number generators are widely used in many applications, ranging from sampling and simulation, fundamental science to cryptography, such as a quantum key distribution system. Among all the previous works, quantum noise from phase fluctuation of laser diodes is one of the most commonly used random source in the quantum random number generation, and many practical schemes based on phase noise with compact systems have been proposed so far. Here, we proposed a new structure of phase noise scheme, utilizing the phase fluctuation from two laser diodes with a slight difference of center wavelength. By analyzing the frequency components and adopting an appropriate band-pass filter, we prove that our scheme extracts quantum noise and filtered other classical noises substantially. Results of a randomness test shows that the extracted random sequences are of good performance. Due to lack of delay-line and the low requirement on other devices in this system, our scheme is promising in future scenarios for miniaturized quantum random number generation systems.
Random number generation is an enabling technology for fields as varied as Monte Carlo simulations and quantum information science. An important application is a secure quantum key distribution (QKD) system; here, we propose and demonstrate an approach to random number generation that satisfies the specific requirements for QKD. In our scheme, vacuum fluctuations of the electromagnetic-field inside a laser cavity are sampled in a discrete manner in time and amplified by injecting current pulses into the laser. Random numbers can be obtained by interfering the laser pulses with another independent laser operating at the same frequency. Using only off-the-shelf opto-electronics and fibre-optics components at 1.5 μμμm wavelength, we experimentally demonstrate the generation of high-quality random bits at a rate of up to 1.5 GHz. Our results show the potential of the new scheme for practical information processing applications.