Semi-device-independent self-testing of unitary operations

TL;DR

This paper introduces a semi-device-independent self-testing protocol for certifying unitary operations using a novel prepare-measure communication game involving shared quantum states and optimal success probabilities.

Contribution

It presents an analytical method for self-testing unitaries in a prepare-measure framework, generalizable to larger systems and other communication games.

Findings

Optimal quantum success probability derived analytically.

Protocol certifies unitaries and measurements in a semi-device-independent setting.

Method can be extended to n-bit prepare-measure random access codes.

Abstract

We present a hitherto unexplored semi-device-independent (SDI) self-testing protocol designed to certify unitary operations within a variant of prepare-measure framework. We consider a communication game which we refer to as a variant of $3$-bit prepare-measure random access code (PMRAC) involving two parties, Alice and Bob, who share a prior two-qubit quantum state. Alice encodes her message by applying unitary operations on her subsystem and sends it to Bob. To decode the message, Bob performs a measurement on the whole system. We demonstrate that the optimal quantum advantage of the variant of $3$-bit PMRAC over the classical bound enables the self-testing of Alice's unitary operations and Bob's measurements. The derivation of the optimal quantum success probability is fully analytical. The approach is so elegant that it can be generalized for any arbitrary $n$-bit PMRAC and may also be extended to other prepare-measure communication games.