Self-testing quantum states and measurements in the prepare-and-measure scenario

TL;DR

This paper develops noise-robust self-testing methods for quantum prepare-and-measure experiments that do not rely on entanglement or Bell inequalities, enabling characterization of quantum states and measurements solely from measurement statistics.

Contribution

It introduces new self-testing techniques for prepare-and-measure scenarios, including analytically optimal tests for qubit-based random access codes, broadening practical quantum device certification.

Findings

Noise-robust self-testing methods for quantum states and measurements.

Analytically optimal self-tests for a 2→1 random access code with qubits.

Methods applicable to experiments without entanglement or Bell inequality violations.

Abstract

The goal of self-testing is to characterize an a priori unknown quantum system based solely on measurement statistics, i.e. using an uncharacterized measurement device. Here we develop self-testing methods for quantum prepare-and-measure experiments, thus not necessarily relying on entanglement and/or violation of a Bell inequality. We present noise-robust techniques for self-testing sets of quantum states and measurements, assuming an upper bound on the Hilbert space dimension. We discuss in detail the case of a $2 \rightarrow 1$ random access code with qubits, for which we provide analytically optimal self-tests. The simplicity and noise robustness of our methods should make them directly applicable to experiments.