# Semi-device-independent characterization of quantum measurements under a minimum overlap assumption

## TL;DR

This paper explores methods to characterize quantum measurement devices in a semi-device-independent setting with minimal assumptions, demonstrating certification of complex measurements and self-testing optimal discrimination strategies.

## Contribution

It introduces new techniques for quantum measurement characterization under limited overlap assumptions, including certification of 3-outcome POVMs and self-testing of optimal discrimination measurements.

## Key findings

- Genuine 3-outcome POVMs can be certified with noise.
- Optimal POVMs for unambiguous state discrimination can be self-tested.
- Methods work under minimal overlap assumptions.

## Abstract

Recently, a novel framework for semi-device-independent quantum prepare-and-measure protocols has been proposed, based on the assumption of a limited distinguishability between the prepared quantum states. Here, we discuss the problem of characterizing an unknown quantum measurement device in this setting. We present several methods to attack this problem. Considering the simplest scenario of two preparations with lower bounded overlap, we show that genuine 3-outcome POVMs can be certified, even in the presence of noise. Moreover, we show that the optimal POVM for performing unambiguous state discrimination can be self-tested.