All the self-testings of the singlet for two binary measurements

TL;DR

This paper characterizes all the criteria for ideal self-testing of the two-qubit singlet state with two measurements and outcomes, showing it matches all extremal quantum correlations achievable by measuring the singlet.

Contribution

It provides a complete characterization of the criteria for ideal self-testing of the singlet, extending beyond known criteria.

Findings

All extremal points of the quantum set for the singlet are identified as self-testing criteria.

The set of criteria for ideal self-testing coincides with extremal quantum correlations.

The results unify and extend previous known self-testing criteria.

Abstract

Self-testing refers to the possibility of characterizing uniquely (up to local isometries) the state and measurements contained in quantum devices, based only on the observed input-output statistics. Already in the basic case of the two-qubit singlet, self-testing is not unique: the two known criteria (the maximal violation of the CHSH inequality and the Mayers-Yao correlations) are not equivalent. It is unknown how many criteria there are. In this paper, we find the whole set of criteria for the ideal self-testing of singlet with two measurements and two outcomes on each side: it coincides with all the extremal points of the quantum set that can be obtained by measuring the singlet.