Semi-Device-Independent Framework Based on Restricted Distrust in Prepare-and-Measure Experiments

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-deviceindependent random number generation are presented.

Contextual advantages and certification for maximum confidence discrimination

“…It is also possible, taking a different point of view of retrodictive quantum theory, to certify the maximum confidence one can have in uncharacterised detectors used for state discrimination. This may be interpreted as a semi-deviceindependent scenario, [28,29] under the assumption that states are well-characterised but the measurements not at all.…”

Receiver-Device-Independent Quantum Key Distribution Protocols

“…Finally, we note our approach shares similarities with the recent work of Ref. [45], where the author investigates correlations in a prepare-and-measure scenario with bounded distrust in the preparations. Specifically, the fidelity of the prepared states with respect to some reference state is lower bounded.…”

Entanglement detection with imprecise measurements

“…Firstly, one can capture the constraints of d-dimensional Hilbert space, on the level of the moment matrix, by numerically sampling states and measurements [31]. Secondly, in scenarios without entanglement, constraints capturing the fidelity of a quantum state with a target can be incorporated into the moment matrix [32]. We adapt the latter to entanglement-based scenarios measurement fidelities as needed for Eq.…”

“…Finally, the framework proposed here for entanglement detection draws inspiration from ideas proposed in semi-device-independent quantum communications. Given that several frameworks for semi-device-independence recently have been proposed [32,[35][36][37][38], there may be other similarly inspired avenues for entanglement detection based on quantitative benchmarks.…”