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.
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.
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.
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.
Abstract Semi-device independent (Semi-DI) quantum random number generators (QRNGs) gained attention for security applications, offering an excellent trade-off between security and generation rate. This paper presents a proof-of-principle time-bin encoding semi-DI QRNG experiments based on a prepare-and-measure scheme. The protocol requires two simple assumptions and a measurable condition: an upper-bound on the prepared pulses’ energy. We lower-bound the conditional min-entropy from the energy-bound and the input–output correlation, determining the amount of genuine randomness that can be certified. Moreover, we present a generalized optimization problem for bounding the min-entropy in the case of multiple input and outcomes, in the form of a semidefinite program. The protocol is tested with a simple experimental setup, capable of realizing two configurations for the ternary time-bin encoding scheme. The experimental setup is easy-to-implement and comprises commercially available off-the-shelf components at the telecom wavelength, granting a secure and certifiable entropy source. The combination of ease-of-implementation, scalability, high security level and output-entropy, make our system a promising candidate for commercial QRNGs.
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.
The rapid rise of quantum computing and quantum internet highlights the irreplaceable importance of high-speed, scalable quantum randomness certification (QRC). However, existing QRC implementations are constrained by quantum measurement limits and integration bottlenecks, leaving both high-speed operation and monolithic implementation unrealized. Here, we demonstrate a monolithically integrated photonic–electronic on-chip source device-independent (SDI) quantum random number generator (QRNG) that achieves a secure bit rate of 583.2 Gbps within a compact 3 mm ×11 mm ×11 mm footprint, marking an advance in both integration and speed, nearly 30 times faster than the best existing integrated SDI implementations. By harnessing measurement-induced quantum uncertainty as a resource for quantum certification, this study resolves the challenge of uniting high-speed certified entropy bounds with full monolithic integration in SDI QRC. A universal entropy bound incorporating high-bandwidth physical constraints enables accurate entropy estimation under integrated conditions. This theoretical framework supports a four-path multi-interference measurement scheme that improves entropy yield and fills a critical gap in digital-layer security under coherent attacks. These contributions are experimentally embodied in a compact photonic–electronic chip that performs NIST-compliant secure entropy extraction, demonstrating the feasibility of combining high-speed performance with full system integration. Compatible with standard optical communication infrastructure, this study sets a new benchmark for scalable high-speed QRC, enabling robust security and broad applicability across quantum computing, the internet, and cryptography.
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.