All pure multipartite entangled states of qubits can be self-tested up to complex conjugation

TL;DR

This paper provides a complete characterization of self-testing for all pure multipartite qubit states, accounting for the fact that some states are only equivalent up to complex conjugation, advancing the understanding of quantum state certification.

Contribution

It introduces a comprehensive self-testing framework for multipartite qubit states, including the complex conjugation ambiguity, which was not previously fully understood.

Findings

All pure multipartite qubit states can be self-tested up to complex conjugation.

The characterization accounts for states not equivalent to their complex conjugates.

The work extends bipartite self-testing results to the multipartite case.

Abstract

Self-testing refers to the certification of quantum states and measurements based entirely on the correlations exhibited by measurements on separate subsystems. In the bipartite case, self-testing of states has been completely characterized, up to local isometries, as there exist protocols that self-test arbitrary pure states of any local dimension. Much less is known in the multipartite case, where an important difference with respect to the bipartite case appears: there exist multipartite states that are not equivalent, up to local isometries, to their complex conjugate. Thus, any self-testing characterization must in general be complete up to not only local unitaries, but also complex conjugation. Under these premises, in this work, we give a complete characterization of self-testing in the multipartite qubit case.