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arXiv:2601.08392 · PRX Quantum

On-chip semi-device-independent quantum random number generator exploiting contextuality

Maddalena Genzini, Caterina Vigliar, Mujtaba Zahidy, Hamid Tebyanian, Andrzej Gajda, Klaus Petermann, Lars Zimmermann, Davide Bacco, Francesco Da Ros

quant-phSubmitted Jan 13, 2026• Announced Jan 14, 2026• 0 citations• Revised Jun 15, 2026 (v2)
v1 · Jan 13, 2026v2 · Jun 15, 2026
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Abstract

We present a semi-device-independent quantum random number generator (QRNG) based on the violation of a contextuality inequality, implemented by the integration of two silicon photonic chips. Our system combines a heralded single-photon source with a reconfigurable interferometric mesh to implement qutrit state preparation, transformations, and measurements suitable for testing a KCBS contextuality inequality. This architecture enables the generation of random numbers from the intrinsic randomness of single-photon interference in a complex optical network, while simultaneously allowing a quantitative certification of their security without requiring entanglement. We observe a contextuality violation exceeding the classical bound by more than 10σ, unambiguously confirming non-classical behavior. From this violation, we certify a conditional min-entropy per experimental round of Hmin = 0.077 +- 0.002, derived via a tailored semidefinite-programming-based security analysis. Each measurement outcome therefore contains at least 0.077 +- 0.002 bits of extractable genuine randomness, corresponding to an asymptotic generation rate of 21.7 +- 0.5 bits/s. These results establish a viable route towards general-purpose, untrusted quantum random number generators compatible with practical integrated photonic quantum networks.

Journal reference
PRX Quantum 7, 033022, 2026
DOI
10.1103/62lv-gmsz

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We present a semi-device-independent quantum random number generator (QRNG) based on the violation of a contextuality inequality, implemented by the integration of two silicon photonic chips. Our system combines a heralded single-photon source with a reconfigurable interferometric mesh to implement qutrit state preparation, transformations, and measurements suitable for testing a KCBS contextuality inequality. This architecture enables the generation of random numbers from the intrinsic randomness of single-photon interference in a complex optical network, while simultaneously allowing a quantitative certification of their security without requiring entanglement. We observe a contextuality violation exceeding the classical bound by more than 10σ, unambiguously confirming non-classical behavior. From this violation, we certify a conditional min-entropy per experimental round of Hmin = 0.077 +- 0.002, derived via a tailored semidefinite-programming-based security analysis. Each measurement outcome therefore contains at least 0.077 +- 0.002 bits of extractable genuine randomness, corresponding to an asymptotic generation rate of 21.7 +- 0.5 bits/s. These results establish a viable route towards general-purpose, untrusted quantum random number generators compatible with practical integrated photonic quantum networks.
Data protection and confidentiality have become a serious concern in today’s world. Their security is guaranteed by cryptographic protocols, which heavily rely on random numbers as a measure against predictability. Classically, randomness is generated via complex but deterministic algorithms, which are vulnerable to attacks. Quantum Random Number Generators (QRNGs) have emerged as a promising solution, as they provide true random numbers based on the intrinsic non-deterministic nature of quantum mechanics. However, critical challenges for QRNGs are the certification and quantification of their genuine randomness, especially in the presence of untrusted devices, and their compactness for systematic deployment. In this feasibility study, to face these challenges, we propose to use a silicon-photonic platform, leveraging on the concept of quantum contextuality for a semi-device independent generator. In particular, we use Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality to assess a fundamental property of quantum measurements: that their outcomes depend on the specific measurement context.
Semi-device-independent QRNG frameworks represent a particularly attractive approach, combining strong security guarantees with high randomness generation rates while relying only on reduced and practical physical assumptions. A recently proposed approach based on photon-number constraints is particularly suited to photonic implementations, where these assumptions can be easily assessed experimentally. Here, we experimentally demonstrate a quantum random number generator within this framework, enabling the direct computation of lower bounds on the certifiable Shannon entropy via semidefinite relaxation techniques. When combined with entropy accumulation methods, this approach enables finite-size randomness certification without assuming independent and identically distributed rounds. We realize the protocol using a four-state coherent-state constellation symmetrically distributed in phase space and measured by heterodyne detection, certifying 0.223 bit per measurement, which is the highest value reported to date for a continuous-variable semi-device-independent QRNG. The implementation combines a low-loss integrated photonic heterodyne receiver with a simple transmitter assembled from commercial components, providing a practical and high-speed architecture for semi-device-independent randomness generation.
Quantum resources offer intrinsic randomness that is valuable for applications such as cryptography, scientific simulation, and computing. Silicon-based photonics chips present an excellent platform for the cost-effective deployment of next-generation quantum systems on a large scale, even at room temperature. Nevertheless, the potential susceptibility of these chips to hacker control poses a challenge in ensuring security for on-chip quantum random number generation, which is crucial for enabling extensive utilization of quantum resources. Here, we introduce and implement an on-chip source-device-independent quantum random number generator (SDI-QRNG). The randomness of this generator is achieved through distortion-free on-chip detection of quantum resources, effectively eliminating classical noise interference. The security of the system is ensured by employing on-chip criteria for estimating security entropy in a practical chip environment. By incorporating a photoelectric package, the SDI-QRNG chip achieves a secure bit rate of 146.2 Mbps and a bare chip rate of 248.47 Gbps, with all extracted secure bits successfully passing the randomness test. Our experimental demonstration of this chip-level SDI-QRNG shows significant advantages in practical applications, paving the way for the widespread and cost-effective implementation of room-temperature secure QRNG, which marks a milestone in the field of QRNG chips.
We present an implementation of a semi-device-independent protocol of the generation of quantum random numbers in a fully integrated silicon chip. The system is based on a prepare-and-measure scheme, where we integrate a partially trusted source of photons and an untrusted single photon detector. The source is a silicon photomultiplier, which emits photons during the avalanche impact ionization process, while the detector is a single photon avalanche diode. The proposed protocol requires only a few and reasonable assumptions on the generated states. It is sufficient to measure the statistics of generation and detection in order to evaluate the min-entropy of the output sequence, conditioned on all possible classical side information. We demonstrate that this protocol, previously realized with a bulky laboratory setup, is totally applicable to a compact and fully integrated chip with an estimated throughput of 6 kHz of the certified quantum random bit rate.
Single-photon entanglement is a peculiar type of entanglement in which two or more degrees of freedom of a single photon are correlated quantum-mechanically. Here, we demonstrate a photonic integrated chip able to generate and manipulate single-photon path-entangled states, using a commercial red LED as light source. A Bell test, in the Clauser, Horne, Shimony, and Holt (CHSH) form, is performed to confirm the presence of entanglement, resulting in a maximum value of the CHSH correlation parameter equal to 2.605±0.004. This allows us to use it as an integrated semi-device independent quantum random number generator able to produce certified random numbers. The certification scheme is based on a Bell’s inequality violation and on a partial characterization of the experimental setup, without the need of introducing any further assumptions either on the input state or on the particular form of the measurement observables. In the end a min-entropy of 33% is demonstrated.
Quantum random number generators (QRNGs) exploit quantum mechanics to produce true randomness, but practical implementations suffer from device imperfections that can compromise security. We propose a semi–device-independent QRNG based on measurement uncertainty under purity constraints for conditional min-entropy estimation. Our protocol requires no detailed modeling of the two-dimensional source and the countable-dimensional measurement and remains secure against quantum attacks on measurement devices. We uncover an implicit uncertainty relation arising from naturally satisfied purity conditions, define a randomness parameter C using test states, and connect it to an analytical bound on extractable randomness via unitary rotation symmetries of states and measurements. Using the generalized entropy accumulation theorem, we extend the single-round bound to multirounds and obtain composable security against coherent attacks. Implemented on a standard commercial fiber system, our high-tolerance protocol achieves exponential secure randomness expansion and is suitable for integrated-photonic platforms.