Semi-device-independent certification of number of measurements

TL;DR

This paper introduces a semi-device-independent method to certify the minimum number of measurements in a quantum system by testing the compatibility of steering equivalent observables using semidefinite programming hierarchies.

Contribution

It presents a novel approach to certify measurement incompatibility in quantum systems without full device characterization, using a hierarchy of semidefinite programs.

Findings

Successfully certifies the minimum number of measurements in quantum systems.

Provides a practical method for semi-device-independent measurement certification.

Establishes a hierarchy of tests for measurement compatibility.

Abstract

We develop a method for semi-device-independent certification of number of measurements. We achieve this by testing whether Bob's steering equivalent observables (SEO) can be simulated by k measurements, which we do by testing whether they are k-compatible with separable joint observable. This test can be performed with the aid of hierarchy of semidefinite programs, and whenever it fails one can conclude that Alice must have access to at least k + 1 incompatible measurements.