QLunch: Maria Balanzó

Speaker: Maria Balanzó, ICFO Institute of Photonic Sciences

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

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. For instance, there exist multipartite states that are not equivalent, up to local isometries, to their complex conjugate, and thus any certification must in general allow complex conjugation as a degree of freedom.  In this work, we give a complete characterization of self-testing in the multipartite qubit case. On the one hand, for any pure multipartite entangled state that is equivalent, up to local isometries, to its complex conjugate, we describe a correlation that self-tests it. On the other hand, for any state that is not equivalent to its complex conjugate, we describe a correlation that singles out the state up to complex conjugation.