Raffaele D'Avino

In a previous work [Senno et al., Phys. Rev. Lett. 131, 130202 (2023)], we provided a framework to quantify the amount of intrinsic randomness produced by characterized but untrusted prepare-and-measure (P\&M) setups. While the cases of pure state preparations or extremal measurements were shown to be defined by semidefinite programs (SDPs), up until now we were missing computational methods for the general scenario of mixed states and nonextremal measurements. In this work, we present a hierarchy of SDP relaxations to lower bound the device-dependent conditional min-entropy. Benchmarking against known special cases, we find that the first level of the hierarchy already attains the optimal value. We then provide two applications. First, for setups affected by global depolarizing noise, we compute a matching lower bound to the analytical attack derived in [Curran et al., arXiv:2506.22294 (2025)], thus showing its optimality. Finally, we show that restricting the correlations between the P\&M boxes to be classical strictly decreases an adversary's predictive power, already in the most elementary setup of a qubit binary measurement.

Quantum information tasks are often analyzed under varying trust assumptions about the devices involved. The semi-device-independent (SDI) framework offers a balance between needed assumptions and experimental feasibility. In this work, we study the energy-constrained SDI scenario, where the only assumption in a prepare-and-measure setup is an upper bound on the energy of the prepared quantum states. In contrast to previous studies that restricted the preparation and measurement devices to be classically correlated, we show that allowing entanglement strictly enlarges the set of achievable correlations. We identify two operational consequences of this result. The first concerns randomness certification, where we show that allowing the adversary to employ entangled strategies may significantly reduce the amount of certifiable randomness. This includes situations where the amount of randomness drops to zero in the presence of entanglement, while it remains positive when entanglement is excluded. Second, for the task of distinguishing an arbitrary quantum channel from the identity, we show that the known dimension-independent bound on the advantage conferred by entanglement is violated under an energy constraint.