Hamid Tebyanian

**merged with** Thomas Van Himbeeck and Stefano Pironio. Correlations and Randomness Generation based on an Energy Constraint In a previous paper, we introduced a semi-device-independent scheme consisting of an untrusted source sending quantum states to an untrusted measuring device, with the sole assumption that the average energy of the states emitted by the source is bounded. Given this energy constraint, we showed that certain correlations between the source and the measuring device can only occur if the outcomes of the measurement are non-deterministic, i.e., these correlations certify the presence of randomness. In the present paper, we go further and show how to quantify the randomness as a function of the correlations and prove the soundness of a QRNG protocol exploiting this relation. For this purpose, we introduce (1) a semidefinite characterization of the set of quantum correlations, (2) an algorithm to lower-bound the Shannon entropy as a function of the correlations and (3) a proof of soundness using finite trials compatible with our energy assumption.

High-quality randomness underpins modern cryptography, yet real quantum random-number generators (QRNGs) can betray subtle correlations introduced by hardware imperfections and environmental drift. We introduce a quantum-inspired deep-learning framework that detects such residual structure with sensitivities unattainable by clas- sical statistical batteries. The architecture intertwines a hierarchy of fractal-memory recurrent layers, a Kerr-oscillator bifurcation model that projects learned patterns into a quantum Hilbert space, and a topological loss based on persistent homology. Device-specific noise—beam-splitter imbalance, detector dark counts, homodyne electronic noise—is injected during training so that optimisation jointly minimises prediction error, topological divergence and loss of quantum fidelity while a reinforcement signal rewards rapid anomaly discovery. Public DV, CV and IBMQ datasets that satisfy all NIST and Diehard tests nevertheless yield bit- prediction accuracies between 0.72 and 0.83 and KL divergences of 3.9×10−2–5.2×10−2, demonstrating that “true” quantum randomness can harbour exploitable patterns unless carefully characterised and extracted.

This study delves into the validity of quantum mechanical operators in the context of quantum gravity, recognizing the potential need for their generalization. A primary objective is to investigate the repercussions of these generalizations on the inherent non-locality within quantum mechanics, as exemplified by Bell’s inequality. Additionally, the study scrutinizes the consequences of introducing a non-zero minimal length into the established framework of Bell’s inequality. The findings contribute significantly to our theoretical comprehension of the intricate interplay between quantum mechanics and gravity. Moreover, this research explores the impact of quantum gravity on Bell’s inequality and its practical applications within quantum technologies, notably in the realms of device-independent protocols, quantum key distribution, and quantum randomness generation.

Semi-device independent (Semi-DI) quantum random number generators (QRNG) 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 (SDP). 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 (COTS) 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.

Randomness is a fundamental feature of quantum mechanics, which is an invaluable resource for both classical and quantum technologies. Practical quantum random number generators (QRNG) usually need to trust their devices, but their security can be jeopardized in 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 untrusted, 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 post-processing, 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.