Quantum Random Number Generator Achieves 10σ Contextuality Violation On-Chip

The demand for truly random numbers continues to grow with increasing reliance on cryptography and scientific simulation. Maddalena Genzini, Caterina Vigliar, and Mujtaba Zahidy, from the Technical University of Denmark, alongside Hamid Tebyanian, Andrzej Gajda, and Klaus Petermann, demonstrate a novel on-chip quantum random number generator (QRNG) that exploits the principles of quantum contextuality. Their research details a system built from integrated silicon photonic chips, capable of generating random numbers by observing the behaviour of single photons within a reconfigurable optical network. This approach is significant because it allows for certification of randomness without needing to confirm entanglement, offering a pathway to more practical and trustworthy QRNGs. The team’s device achieves a certified min-entropy of 0.077 ±0.002 bits per experimental round, corresponding to a generation rate of 21.7 ±0.5 bits per second, and represents a substantial step towards deployable, device-independent random number generation.

The research team achieved a semi-device-independent design, meaning the system’s security relies on fewer assumptions about its internal components than fully trusted QRNGs, yet avoids the stringent requirements of fully device-independent schemes. This breakthrough combines a heralded single-photon source with a reconfigurable interferometric mesh implemented on two silicon photonic chips, enabling the generation of truly random numbers from the inherent randomness of single-photon interference. The study unveils an architecture capable of preparing, transforming, and measuring qutrit states, quantum systems with a three-dimensional state space, specifically designed to test the Klyachko-Can-Binicio glu-Shumovsky (KCBS) contextuality inequality.

Experiments show a clear violation of this inequality, exceeding the classical bound by more than 10σ, unambiguously confirming non-classical behaviour within the system. This contextuality violation forms the basis for certifying the genuine randomness of the generated numbers, independent of detailed knowledge of the device’s internal workings. Researchers certified a conditional min-entropy of Hmin = 0.077 ±0.002 per experimental round, calculated using a tailored semidefinite-programming-based analysis. This signifies that each measurement outcome contains at least 0.077 ±0.002 bits of extractable genuine randomness, translating to an asymptotic generation rate of 21.7 ±0.5 bits per second.

The work establishes a practical pathway towards creating general-purpose, untrusted random number generators suitable for integration into existing and future photonic quantum networks. This integrated semi-device-independent QRNG significantly reduces the physical footprint of quantum systems while simultaneously enhancing security. The research opens possibilities for deploying robust random number generation on remote, untrusted hardware, with potential applications in areas such as quantum key distribution systems and secure communication protocols. By combining the advantages of integrated photonics with contextuality-based certification, the team has created a viable solution for generating high-quality random numbers essential for a range of critical computational tasks.

Qutrit Interference for Certified Random Number Generation

The research team pioneered a semi-device-independent quantum random number generator (QRNG) by leveraging a violation of a contextuality inequality. This innovative system integrates two silicon photonic chips, combining a heralded single-photon source with a reconfigurable interferometric mesh to prepare, transform, and measure qutrit states. This architecture facilitates the generation of random numbers directly from the inherent randomness of single-photon interference within a complex optical network, while simultaneously enabling quantitative certification of randomness without requiring entanglement. Experiments employed a silicon-based programmable photonic processor, iPronics Smartlight, comprising 72 programmable unit cells arranged in a hexagonal mesh.

Each unit cell contains a tunable Mach-Zehnder interferometer with internal thermo-optic phase shifters, granting precise control over induced relative and global phases for arbitrary SU(2) transformations between optical modes. The study meticulously accounted for system loss, identifying contributions of approximately 11 dB from the heralded single-photon source chip and a dominant 27 dB from the interferometer mesh chip, primarily due to in- and out-coupling inefficiencies and propagation losses of 0.5 dB per unit cell. To verify qutrit state preparation, scientists performed quantum state tomography using a maximum likelihood estimation procedure. Measurements were conducted in three mutually unbiased bases, computational, Fourier, and a derived basis, utilizing nine averaged coincident photon count measurements.

The resulting data defined a likelihood function numerically optimized to reconstruct the density matrix in the Gell-Mann representation, with 10-minute acquisition intervals used for averaging. This approach yielded a certified conditional min-entropy of Hmin = 0.077 ±0.002 per experimental round, demonstrating that each measurement outcome contains at least 0.077 ±0.002 bits of extractable genuine randomness. The system achieves an asymptotic generation rate of 21.7 ±0.5 bits/s, establishing a viable pathway for practical, untrusted random number generators compatible with integrated photonic networks.

Contextuality Violation Enables Certified Quantum Randomness

Scientists achieved a significant breakthrough in quantum random number generation, demonstrating a semi-device-independent QRNG built upon the violation of a contextuality inequality. The research team integrated two silicon photonic chips to create a system capable of qutrit state preparation, transformation, and measurement, essential for testing the Klyachko-Can-Binicio glu-Shumovsky (KCBS) contextuality inequality. Experiments revealed a contextuality violation exceeding the classical bound by more than 10σ, unambiguously confirming non-classical behaviour within the system and paving the way for certified randomness. This robust result validates the potential for generating truly random numbers from the inherent randomness of single-photon interference.

Measurements confirm a conditional min-entropy of Hmin = 0.077 ±0.002 per experimental round, derived through a tailored semidefinite-programming-based analysis. This signifies that each measurement outcome contains at least 0.077 ±0.002 bits of extractable genuine randomness, a crucial metric for secure applications. The team recorded an asymptotic generation rate of 21.7 ±0.5 bits per second, demonstrating a substantial increase in speed compared to many existing device-independent approaches. This achievement is particularly notable as it circumvents the need for high-quality entanglement or space-like separation, common limitations in other QRNG designs.

The work establishes a viable route towards general-purpose, untrusted random number generators compatible with practical integrated photonic networks. By utilising a heralded single-photon source and a reconfigurable interferometric mesh, the researchers implemented a qutrit system, a three-dimensional quantum system, to test the KCBS inequality. The observed violation of −3.84 ±0.08, compared to the classical limit of −3, provides strong evidence of quantum contextuality and underpins the certified randomness. This integrated approach significantly reduces the physical footprint of the QRNG system, making it suitable for deployment in distributed quantum systems.

This breakthrough delivers a promising platform for applications requiring high-quality randomness, such as Monte Carlo simulations, neural network weighting, and secure communication protocols. Tests prove the feasibility of embedding this semi-DI QRNG within larger quantum networks, including photonic quantum key distribution systems and distributed quantum computing platforms, offering a secure and efficient solution for generating random numbers on remote, untrusted hardware. The research highlights the potential of silicon photonics for realising practical and scalable quantum technologies.

Silicon Photonic QRNG Demonstrates High Contextuality

This research demonstrates a semi-device-independent quantum random number generator (QRNG) constructed from two silicon photonic chips. The system leverages a violation of a contextuality inequality, specifically the KCBS inequality, to generate random numbers directly from the inherent randomness of single-photon interference. Through careful measurement and analysis, the researchers unambiguously confirmed non-classical behaviour with a contextuality violation exceeding the classical bound by over 10σ, certifying a min-entropy of 0.077 ±0.002 bits per experimental round. The achieved random number generation rate is 21.7 ±0.5 bits per second, validated using the NIST SP 800-22 test suite, establishing a pathway towards practical, untrusted QRNGs compatible with integrated photonic networks.

The authors acknowledge a limitation stemming from potential compatibility issues with observables within the KCBS inequality, which they addressed through established modifications to the inequality. Future work could focus on increasing the generation rate by integrating brighter photon sources and optimising the interferometric mesh architecture, potentially reaching rates exceeding 120 kbits/s. This work also lays the groundwork for on-demand contextuality verification within reprogrammable photonic hardware, opening possibilities for applications in quantum key distribution and randomness amplification.