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IEEE Journal of Selected Topics in Quantum Electronics

Continuous-Variable Source-Independent Quantum Random Number Generator With Phase-Insensitive Detection

Hongyi Zhou

Published Mar 19, 2025• 1 citation
Publisher

Abstract

Quantum random number generators (QRNGs) harness quantum mechanical unpredictability to produce true randomness, which is crucial for cryptography and secure communications. Among various QRNGs, source-independent QRNGs (SI-QRNGs) relax the trust on the quantum source, allowing for flexible use of advanced detectors to achieve high randomness generation rates. Continuous-variable (CV) SI-QRNGs, in particular, hold promise for practical deployment due to their simplicity and randomness generation rates comparable to trusted-device QRNGs. In this work, we propose a novel CV-SI-QRNG scheme based on phase-insensitive detections, and provide security proof based on semi-definite programming (SDP). We introduce a dimension reduction technique, which rigorously reduces an infinite-dimensional SDP problem to a finite-dimensional one, enabling efficient computation while maintaining valid randomness lower bound. We further validate our method through simulations. These results demonstrate the feasibility of our framework, paving the way for practical and simple SI-QRNG implementations.

DOI
10.1109/jstqe.2025.3552899

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Quantum random number generators (QRNGs) harness quantum mechanical unpredictability to produce true randomness, which is crucial for cryptography and secure communications. Among various QRNGs, source-independent QRNGs (SI-QRNGs) relax the trust on the quantum source, allowing for flexible use of advanced detectors to achieve high randomness generation rates. Continuous-variable (CV) SI-QRNGs, in particular, hold promise for practical deployment due to their simplicity and randomness generation rates comparable to trusted-device QRNGs. In this work, we propose a novel CV-SI-QRNG scheme based on phase-insensitive detections, and provide security proof based on semi-definite programming (SDP). We introduce a dimension reduction technique, which rigorously reduces an infinite-dimensional SDP problem to a finite-dimensional one, enabling efficient computation while maintaining valid randomness lower bound. We further validate our method through simulations. These results demonstrate the feasibility of our framework, paving the way for practical and simple SI-QRNG implementations.
Quantum random number generators (QRNGs) harness quantum mechanical unpredictability to produce true randomness, which is crucial for cryptography and secure communications. Among various QRNGs, source-independent QRNGs (SI-QRNGs) relax the trust on the quantum source, allowing for flexible use of advanced detectors to achieve high randomness generation rates. Continuous-variable (CV) SI-QRNGs, in particular, hold promise for practical deployment due to their simplicity and randomness generation rates comparable to trusted-device QRNGs. In this work, we propose a novel CV-SI-QRNG scheme with a single phase-insensitive detector, and provide security proof based on semi-definite programming (SDP). We introduce a dimension reduction technique, which rigorously reduces an infinite-dimensional SDP problem to a finite-dimensional one, enabling efficient computation while maintaining valid randomness lower bound. We further validate our method through simulations. These results demonstrate the feasibility of our framework, paving the way for practical and simple SI-QRNG implementations.
Continuous-variable source-independent quantum random number generators offer the highest generation rates among semi-device-independent protocols. In reality, the protocol design is limited due to permissible measurement configurations. In this work, we propose a rigorous security proof framework that accommodates general, infinite-dimensional positive-operator-valued measures. Building upon the numerical security proof framework, we evaluate the randomness lower bound by maximizing the eavesdropper's guessing probability. Specifically, we transform the inherently infinite-dimensional semidefinite program in Fock space into a tractable finite-dimensional one, rigorously proving that latter provides a strict upper bound to the guessing probability of the original infinite-dimensional problem. Our framework showcases its capability by certifying secure randomness using unbalanced homodyne detection with only a single quadrature measurement, thereby bypassing the traditional requirement of measuring two conjugate quadratures such as XXX and PPP. We experimentally validate our protocol on an optical platform using vacuum and weak coherent states, achieving a maximum secure randomness extraction of 1.11 bits per sample and an ultra-high generation rate of 1.776 Gbps. This work provides a flexible design for practical, high-speed quantum random number generators.
Quantum random number generators (QRNGs) produce true random numbers based on the inherent randomness of quantum theory, rendering them a foundational segment of quantum cryptography. Distinguished from trusted-device QRNGs whose security depends on characterized devices, semi-device-independent (semi-DI) QRNGs permit partial devices to be defective or even maliciously manipulated, which achieves a good trade-off between generation rate and security. In this paper, we propose a semi-DI QRNG that resists general attacks while accounting for finite-size effects. The protocol requires no rigorous characterization of the source and measurement devices other than limiting the energy of the emitted states, significantly reducing the demands on practical QRNG systems. Leveraging the tight Kato inequality for correlated variables, we show that our protocol generates more randomness than it consumes. Furthermore, we demonstrate the scheme on a continuous-variable system with ternary inputs of states. Heterodyne detection is employed to enable phase compensation through data postprocessing, alleviating the stringent requirement on system stability. The system operates at 100 MHz, achieving a net random number generation rate of 1.165 Mbps at 5.3x10^9 rounds. Our work offers a promising approach to achieve both the robust security and high generation rate with a simple experimental setup.
Continuous-variable source-independent quantum random-number generators (CV-SI-QRNGs) generate high-speed secure random numbers without any assumptions about source. Recently, Smith et al. [Phys. Rev. A 99, 062326 (2019)] proposed a CV-SI-QRNG with phase-randomized local oscillator (LO) protocol, which does not require additional active optical components, thus reducing the complexity of the CV-SI-QRNG setup and attracting widespread attention. However, the trusted but imperfect sampling device used in CV-SI-QRNG has not yet been fully investigated, which will lead to performance degradation and security problems. In this work, we investigate the influence of imperfect sampling devices on the CV-SI-QRNG with phase-randomized LO, including the finite-sampling bandwidth, finite-sampling precision, and finite-size effect. Simulation results show that practical imperfections in the sampling device will affect the estimation of lower bound on the conditional min-entropy and reduce the extractable randomness. To improve the performance of CV-SI-QRNG and prevent such information leakages, we also provide some corresponding countermeasures. Our work highlights the influences of imperfect sampling devices on the performance and security of practical CV-SI-QRNG systems, which helps to improve their robustness and practicality.
Abstract As a fundamental phenomenon in nature, randomness has a wide range of applications in the fields of science and engineering. Among different types of random number generators (RNG), quantum random number generator (QRNG) is a kind of promising RNG as it can provide provable true random numbers based on the inherent randomness of fundamental quantum processes. Nevertheless, the randomness from a QRNG can be diminished (or even destroyed) if the devices (especially the entropy source devices) are not perfect or ill-characterized. To eliminate the practical security loopholes from the source, source-independent QRNGs, which allow the source to have arbitrary and unknown dimensions, have been introduced and become one of the most important semi-device-independent (DI) QRNGs. Herein a method that enables ultra-fast unpredictable quantum random number generation from quadrature fluctuations of quantum optical field without any assumptions on the input states is proposed. Particularly, to estimate a lower bound on the extractable randomness that is independent from side information held by an eavesdropper, a new security analysis framework is established based on the extremality of Gaussian states, which can be easily extended to design and analyze new semi-DI continuous variable QRNG protocols. Moreover, the practical imperfections of the QRNG including the effects of excess noise, finite sampling range, finite resolution and asymmetric conjugate quadratures are taken into account and quantitatively analyzed. Finally, the proposed method is experimentally demonstrated to obtain high secure random number generation rates of 15.07 Gbits s −1 in off-line configuration and can potentially achieve 6 Gbits s −1 by real-time post-processing.
Heterodyne-based continuous-variable source-independent quantum random number generator (CV-SI-QRNG) can produce true random numbers without any assumptions on source. However, practical implementations always contain imperfections, which will greatly influence the extractable randomness and even open loopholes for eavesdroppers to steal information about the final output. In this work, based on the theoretical model, we systematically analyzed the effects of imperfect implementations on the practical security of heterodyne-based CV-SI-QRNG. The influences of local oscillator (LO) fluctuation under imbalanced heterodyne detection are first analyzed. The simulation results show that the lower bound of extractable randomness will be overestimated without considering the influence of LO fluctuation, which will threaten the practical security of CV-SI-QRNG system. Moreover, we analyze the effects of the degree of imbalance and the magnitude of LO fluctuation on evaluating the extractable randomness. Finally, we investigate the impact of an imperfect phase modulator on the practical security of CV-SI-QRNG and find it will reduce the extractable randomness. Our analysis reveals that one should carefully consider the imperfections in the actual implementations of CV-SI-QRNGs.