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arXiv:2606.31027

Continuous-Variable Source-Independent Quantum Random Number Generation with General POVMs

Hongyi Zhou, Yu Han, Qiechun Chen, Leilei Huang

quant-phSubmitted Jun 30, 2026• Announced Jul 1, 2026• 0 citations
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Abstract

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 $X$ and $P$. 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.

Comments
11 pages, 3 figures

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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) 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.
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.
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.
Quantum random numbers have an incomparable advantage over pseudo-random numbers since randomness originates from intrinsic property of quantum mechanics. The generation rate and the security of quantum random numbers are two significant indicators of a quantum random number generator (QRNG) for practical applications. Here we propose a mutually testing source-device-independent QRNG by simultaneously measuring a pair of conjugate quadratures from two separate parts of an untrusted continuous-variable quantum state. The amounts of randomness of the quadratures can be mutually estimated by each other via entropic uncertainty principle. Instead of randomly toggling between the conjugate quadratures of one state for collecting different types of data, two quadratures can generate check data and raw bits simultaneously and continuously in this mutually testing manner, which enhances the equivalent generation rate of private random bits to around 6 Gbit/s with a 7.5 mW laser beam. Moreover, the overall security is also improved by adjusting the conditional min-entropy in real time according to the continually monitored fluctuations of the local oscillator and the randomly measured electronic noise of homodyne detectors.
Random numbers are commonly used in many different fields, ranging from simulations in fundamental science to security applications. In some critical cases, as Bell's tests and cryptography, the random numbers are required to be both private and to be provided at an ultra-fast rate. However, practical generators are usually considered trusted, but their security can be compromised in case of imperfections or malicious external actions. In this work we introduce an efficient protocol which guarantees security and speed in the generation. We propose a source-device-independent protocol based on generic Positive Operator Valued Measurements and then we specialize the result to heterodyne measurements. Furthermore, we experimentally implemented the protocol, reaching a secure generation rate of 17.42 Gbit/s, without the need of an initial source of randomness. The security of the protocol has been proven for general attacks in the finite key scenario.