Entanglement in the energy-constrained prepare-and-measure scenario: applications to randomness certification and channel discrimination

TL;DR

This paper investigates how entanglement affects correlations and randomness certification in an energy-constrained semi-device-independent quantum scenario, revealing that entanglement can both reduce certifiable randomness and enhance channel discrimination.

Contribution

It demonstrates that entanglement enlarges the set of correlations in energy-constrained SDI scenarios and impacts the effectiveness of randomness certification and channel discrimination.

Findings

Entanglement enlarges the set of achievable correlations.

Allowing entanglement can reduce certifiable randomness, even to zero.

Entanglement can improve channel discrimination beyond known bounds.

Abstract

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.