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Photonics

Exploiting a Multi-Mode Laser in Homodyne Detection for Vacuum-Fluctuation-Based Quantum Random Number Generator

Sooyoung Park, Sanghyuk Kim, Chul-Woo Park, Jeong Woon Choi

Published Aug 25, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.3390/photonics12090851

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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.
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.
Unpredictable random number (RN) generation is an essential technology for cryptographic applications. Quantum RN generators (QRNGs) have attracted significant attention owing to their generation of RNs utilizing the randomness guaranteed by quantum mechanics. Vacuum fluctuations are a promising entropy source of quantum randomness. These are detected using a homodyne setup with a laser source and a beam splitter. QRNGs based on vacuum fluctuations can generate RNs at a high-speed and in a stable manner. This paper reports a high-speed spatially multiplexed QRNG based on vacuum fluctuations using a single semiconductor laser diode and an integrated optical beam splitter. The QRNG obtained four independent vacuum fluctuations across a wide bandwidth of over 2 GHz. The RNs were extracted in parallel using a field-programmable gate array with analog-to-digital converters. An aggregated real-time RN generation rate of 4×12.5 Gbit/s was achieved. The generated RNs passed a randomness test based on NIST SP800-90B.
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. In the case of trusted devices, true randomness could be generated from a mixed state ρ so long as the system entangled with ρ is well protected. We propose a random number generation scheme based on measuring the quadrature fluctuations of a single mode thermal state using an optical homodyne detector. By mixing the output of a broadband amplified spontaneous emission (ASE) source with a single mode local oscillator (LO) at a beam splitter and performing differential photo-detection, we can selectively detect the quadrature fluctuation of a single mode output of the ASE source, thanks to the filtering function of the LO. Experimentally, a quadrature variance about three orders of magnitude larger than the vacuum noise has been observed, suggesting this scheme can tolerate much higher detector noise 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. A Toeplitz-hashing extractor is applied to generate unbiased random bits from the Gaussian distributed raw data, achieving an efficiency of 5.12 bits per sample. The output of the Toeplitz extractor successfully passes all the NIST statistical tests for random numbers.
Quantum random number generators (QRNGs) based on quadrature measurements of the vacuum have so far used balanced homodyne detection to obtain a source of high entropy. Here we propose a simple direct detection measurement scheme using only a laser and a photodiode that still extracts randomness from vacuum fluctuations. We prove the security of the QRNG based on a reduced set of assumptions in comparison to previous security proofs for quadrature detection as our proof does not require the laser or electronic noise to be Gaussian. Using a low-cost setup based on a vertical-cavity surface-emitting laser we experimentally implement the QRNG scheme. We propose a system characterization method, apply it to our implementation and demonstrate a real-time randomness extraction rate of 3.41 Gbit per second. The unique combination of speed, low cost, and rigorous security proof gives our QRNG design a large potential for a wide-scale usage in a variety of applications ranging from quantum key distribution to mobile applications and internet of things.
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.
We present a high-speed continuous-variable quantum random number generator (QRNG) based on heterodyne detection of vacuum fluctuations. The scheme follows a source-device-independent (SDI) security model in which the entropy originates from quantum measurement uncertainty and no model of the source is required; security depends only on the trusted measurement device and the calibrated discretization, and thus remains valid even under adversarial state preparation. The optical field is split by a 90∘^\circ∘ optical hybrid and measured by two balanced photodiodes to obtain both quadratures of the vacuum state simultaneously. The analog outputs are digitized using a dual-channel 12-bit analog-to-digital converter operating at a sampling rate of 3.2 GS/s per channel, and processed in real time by an FPGA implementing Toeplitz hashing for randomness extraction. The quantum-to-classical noise ratio was verified through calibrated power spectral density measurements and cross-checked in the time domain, confirming vacuum-noise dominance within the 1.6 GHz detection bandwidth. After extraction, the system achieves a sustained generation rate of Rnet=33.92 Gbit/sR_{\rm net}= 33.92~\mathrm{Gbit/s}Rnet​=33.92 Gbit/s of uniformly distributed random bits, which pass all NIST and Dieharder statistical tests. The demonstrated platform provides a compact, FPGA-based realization of a practical heterodyne continuous-variable source-independent QRNG suitable for high-rate quantum communication and secure key distribution systems.