Semi-device-independent framework based on restricted distrust in prepare-and-measure experiments

TL;DR

This paper introduces a semi-device-independent framework for prepare-and-measure quantum experiments that allows tuning distrust levels, enabling certification, advantage demonstration, and random number generation without assuming Hilbert space dimension.

Contribution

It develops a novel semi-device-independent approach that bounds quantum correlations and optimizes quantum state discrimination under distrust constraints.

Findings

Quantum advantages are demonstrated under bounded distrust.

Efficient semi-device-independent random number generation schemes are proposed.

Bounds on quantum correlations are established from both inside and outside.

Abstract

A semi-device-independent framework for prepare-and-measure experiments is introduced in which an experimenter can tune the degree of distrust in the performance of the quantum devices. In this framework, a receiver operates an uncharacterised measurement device and a sender operates a preparation device that emits states with a bounded fidelity with respect to a set of target states. No assumption on Hilbert space dimension is required. The set of quantum correlations is investigated and bounded from both the interior and the exterior. Furthermore, the optimal performance of quantum state discrimination with bounded distrust is derived and applied to certification of detection efficiency. Quantum-over-classical advantages are demonstrated and the magnitude of distrust compatible with such advantages is explored. Finally, efficient schemes for semi-device-independent random number generation are developed.