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Certified Quantum Randomness with Coherent Detection

Vitor Lucas O. Sena, Moisés Alves, Santiago Zamora, Tailan S. Sarubi, A. de Oliveira, Alexandre B. Tacla

Published May 25, 2026• 0 citations
Publisher

Abstract

In this work, we analyze a semi-device-independent technique for quantum random number generation (QRNG) certification based on coherent detection. We consider a prepare-and-measure scenario, in which pure quantum states are prepared and sequentially measured using homodyne detection, a continuous-variable measurement, and evaluate dimension witness (DW) inequalities to certify quantum randomness. We extend the DW framework to this continuous-variable setting through phase-space binning optimization and demonstrate that symmetric binning maximizes DW violation across single-, double-, and triple-partition configurations. We additionally explore heterodyne (double homodyne) detection as a complementary coherent measurement; no witness violation is observed under this scheme for several discretization schemes. This work provides additional analysis to the study of certifiable QRNG based on homodyne detection, a mature and widely available technology with natural applicability in secure network communications.

DOI
10.5753/wqunets.2026.23540

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In this work, we analyze a semi-device-independent technique for quantum random number generation (QRNG) certification based on coherent detection. We consider a prepare-and-measure scenario, in which pure quantum states are prepared and sequentially measured using homodyne detection, a continuous-variable measurement, and evaluate dimension witness (DW) inequalities to certify quantum randomness. We extend the DW framework to this continuous-variable setting through phase-space binning optimization and demonstrate that symmetric binning maximizes DW violation across single-, double-, and triple-partition configurations. We additionally explore heterodyne (double homodyne) detection as a complementary coherent measurement; no witness violation is observed under this scheme for several discretization schemes. This work provides additional analysis to the study of certifiable QRNG based on homodyne detection, a mature and widely available technology with natural applicability in secure network communications.
Randomness is fundamental for secure communication and information processing. While continuous-variable optical systems offer an attractive platform for this task, certifying genuine quantum randomness in such setups remains challenging. We present a semi-device-independent scheme for randomness certification tailored to continuous-variable implementations, where the dimension assumption is operationally implemented by restricting state preparations to the two-level Fock subspace. Using standard homodyne and displacement-based measurements, we show that simple optical setups can achieve dimension-witness violations that certify positive min-entropy, even in the presence of realistic losses and misaligned reference frames. These results demonstrate that practical and scalable quantum randomness generation is achievable with minimal experimental complexity on continuous-variable platforms.
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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.
Randomness is a fundamental feature of quantum mechanics, which is an invaluable resource for both classical and quantum technologies. Practical quantum random-number generators (QRNGs) usually need to trust their devices, but their security can be jeopardized in the case of imperfections or malicious external actions. In this work, we present a robust implementation of a semi-device-independent QRNG that guarantees both security and fast generation rates. The system works in a prepare-and-measure scenario, where measurement and source are uncharacterized, but a bound on the energy of the prepared states is assumed. Our implementation exploits heterodyne detection, which offers increased generation rate and improved long-term stability compared to alternative measurement strategies. In particular, due to the tomographic properties of heterodyne measurement, we can compensate for fast phase fluctuations via postprocessing, avoiding complex active phase-stabilization systems. As a result, our scheme combines high security and speed with a simple setup featuring only commercial-off-the-shelf components, making it an attractive solution in many practical scenarios.
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.