Coarse-grained self-testing

TL;DR

This paper introduces a coarse-grained self-testing method that certifies properties of many-body quantum systems, demonstrating that maximal violation of a generalized Bell inequality uniquely identifies many-body singlet states.

Contribution

It extends self-testing to many-body systems, showing how to certify complex quantum states using a generalized Bell inequality.

Findings

Maximal violation of the many-body Bell inequality certifies the many-body singlet state.

The approach can certify mixtures of orthogonal states within the singlet manifold.

The method scales exponentially with the number of particles.

Abstract

Self-testing is a device-independent method that usually amounts to show that the maximal quantum violation of a Bell's inequality certifies a unique quantum state, up to some symmetries inherent to the device-independent framework. In this work, we enlarge this approach and show how a coarse-grained version of self-testing is possible in which physically relevant properties of a many-body system are certified. For that we study a Bell scenario consisting of an arbitrary number of parties and show that the membership to a set of (entangled) quantum states whose size grows exponentially with the number of particles can be self-tested. Specifically, we prove that a many-body generalization of the chained Bell inequality is maximally violated if and only if the underlying quantum state is equal, up to local isometries, to a many-body singlet. The maximal violation of the inequality therefore certifies any statistical mixture of the exponentially-many orthogonal pures states spanning the singlet manifold.