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Effect of Classical Noise on Quantum Random Number Generation Based on Vacuum Fluctuation

Ken Tanizawa

Published Feb 21, 2025• 0 citations
OpenAlex

Abstract

A quantum random number generator (QRNG) utilizes quantum mechanical phenomena, such as photon superposition and vacuum fluctuation, to produce truly unpredictable random numbers. This study analyzes the effect of classical noise in a QRNG based on vacuum fluctuation, focusing on thermal noise and relative intensity noise (RIN) in an entropy source consisting of a laser source and balanced homodyne receiver. Numerical analysis shows that RIN significantly impacts QRNG performance when the error in the splitting ratio of a half beam splitter in the receiver exceeds 0.5 dB. This study indicates design guidelines for QRNG setups based on vacuum fluctuation.

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A quantum random number generator (QRNG) utilizes quantum mechanical phenomena, such as photon superposition and vacuum fluctuation, to produce truly unpredictable random numbers. This study analyzes the effect of classical noise in a QRNG based on vacuum fluctuation, focusing on thermal noise and relative intensity noise (RIN) in an entropy source consisting of a laser source and balanced homodyne receiver. Numerical analysis shows that RIN significantly impacts QRNG performance when the error in the splitting ratio of a half beam splitter in the receiver exceeds 0.5 dB. This study indicates design guidelines for QRNG setups based on vacuum fluctuation.
Quantum random number generator (QRNG) allows obtaining true random bit sequences. In QRNG based on quantum nature of vacuum, optical beam splitter with two inputs and two outputs is normally used. We compare mathematical descriptions of spatial beam splitter and fiber Y-splitter in the quantum model for QRNG, based on homodyne detection. These descriptions were identical, that allows to use fiber Y-splitters in practical QRNG schemes, simplifying the setup. Also we receive relations between the input radiation and the resulting differential current in homodyne detector. We experimentally demonstrate possibility of true random bits generation by using QRNG based on homodyne detection with Y-splitter.
To realize a vacuum-fluctuation-based quantum random number generator (QRNG), various implementations can be explored to improve efficiency and practicality. In this study, we employed a multi-mode (MM) laser as the local oscillator in a vacuum-fluctuation QRNG and compared its performance with that of a conventional single-mode (SM) laser. Despite experiencing frequency-mode hopping, the MM laser successfully interfered with the vacuum state, similar to the SM reference. The common-mode rejection ratio of the balanced homodyne detection setup exceeded 35 dB for all laser sources. The digitized raw data were processed with a cryptographic hash function to generate full-entropy data. These outputs passed both the independent and identically distributed test recommended in NIST SP 800-90B and the statistical test suite under the SP 800-22 guideline, confirming their quality as quantum random numbers. Our results demonstrate that full-entropy data derived from either SM or MM lasers are applicable to systems requiring high-quality randomness, such as quantum key distribution. This study represents the first demonstration of an MM-laser-based vacuum-fluctuation QRNG, achieving a generation rate of 10 Gbps and indicating potential for compact and practical implementation.
Quantum random number generators (QRNGs) harness the intrinsic randomness in measurement processes: the measurement outputs are truly random given the input state is a superposition of the eigenstates of the measurement operators. We show in the case of trusted devices, genuine randomness could be generated even when the input to the detector is a mixed state. We propose a random number generation scheme based on measuring the quadrature fluctuations of a single mode thermal state with an optical homodyne detector. By interfering a broadband incoherent source with a single mode local oscillator at a beam splitter and performing differential photodetection, we can selectively detect the quadrature fluctuations of a single mode of the incoherent source, thanks to the filtering function introduced by the local oscillator. Experimentally, a quadrature variance about three orders of magnitude larger than the vacuum noise is observed from an amplified spontaneous emission source, suggesting this scheme can tolerate much high technical noises in comparison with QRNGs based on measuring the vacuum noise. The high quality of this entropy source is evidenced by the small correlation coefficients of the acquired data.
Abstract We present a quantum random number generator (QRNG) based on vacuum fluctuations that meets the statistical and structural entropy source validation criteria defined in NIST standards. We measured how optical imbalance in a balanced homodyne detector affects the dominance of vacuum fluctuations over the quadrature-phase noise of the local oscillator. Based on this analysis, we developed a simple and direct method to quantify the relative strength of vacuum noise, enabling precise balancing of the detector to maximize the vacuum fluctuation contribution. Our approach ensures that the raw entropy exhibits negligible auto-correlation and that the output samples are independent and identically distributed (i.i.d.), without relying on external post-processing beyond standard NIST-approved conditioning. Following a symbol-space reduction strategy guided by NIST SP 800-90B, we extract high-quality 8-bit entropy samples from 16-bit raw data. To produce full-entropy outputs, the samples are processed using the 384-bit version of the Secure Hash algorithm 3 (SHA3-384). The resulting quantum random numbers successfully pass all tests in the NIST statistical test suite (NIST SP 800-22) and achieve a generation rate of approximately 4 Gbps. This work demonstrates a practical and fully standards-aligned QRNG implementation using only vacuum fluctuations and vetted conditioning.
A quantum random-number generator (QRNG) can theoretically generate unpredictable random numbers with perfect devices and is an ideal and secure source of random numbers for cryptography. However, the practical implementations always contain imperfections, which will greatly influence the randomness of the final output and even open loopholes to eavesdroppers. Recently, Thewes et al. experimentally demonstrated a continuous-variable eavesdropping attack, based on heterodyne detection, on a trusted continuous-variable QRNG in Phys. Rev. A 100, 052318 (2019), yet like in many other practical continuous-variable QRNG studies, they always supposed the local oscillator was stable and ignored its fluctuation, which might lead to security threats such as wavelength attack. In this work, based on the theory of the conditional min-entropy, imperfections of the practical security of continuous-variable QRNGs are systematically analyzed, especially the local oscillator fluctuation under imbalanced homodyne detection. Experiments of a practical QRNG based on vacuum fluctuation are demonstrated to show the influence of local oscillator fluctuation on the total measurement noise variances and the practical conditional min-entropy with beam splitters of different transmittances. Moreover, a local oscillator monitoring method is proposed for the practical continuous-variable QRNG, which can be used to calibrate the practical conditional min-entropy.
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.