# Semi-device-independent self-testing of unsharp measurements

## TL;DR

This paper introduces a semi-device-independent method to self-test unsharp quantum measurements, demonstrating their advantages over sharp measurements and providing robust characterization techniques using semidefinite programming.

## Contribution

It presents a novel scheme for self-testing unsharp measurements and introduces a semidefinite programming method for bounding quantum correlations in sequential measurement scenarios.

## Key findings

- Unsharp measurements outperform sharp ones in certain scenarios.
- All two-outcome qubit measurements can be robustly characterized.
- The method improves security analysis in quantum key distribution.

## Abstract

Unsharp quantum measurements provide a resource in scenarios where one faces the trade-off between information gain and disturbance. In this work we introduce a prepare-transform-measure scenario in which two-outcome unsharp measurements outperform their sharp counterparts, as well as any stochastic strategy involving dichotomic projective measurements. Based on that, we propose a scheme for semi-device-independent self-testing of unsharp measurements and show that all two-outcome qubit measurements can be characterized in a robust way. Along with the main result, in this work we introduce a method, based on semidefinite programming, for bounding quantum correlations in scenarios with sequential measurements of length two. This method can also be applied to refine security analysis of the semi-device-independent one-way quantum key distribution. We also present new information gain-disturbance relation for pairs of dichotomic measurements.