The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing

Aloy, A.; Fadel, M.; Tura Brugués, J. (2021)

Article / Letter to editor

In this paper, we present a method to solve the quantum marginal problem for symmetric d-level systems. The method is built upon an efficient semi-definite program that uses the compatibility conditions of an m-body reduced density with a global n-body density matrix supported on the symmetric space. We illustrate the applicability of the method in central quantum information problems with several exemplary case studies. Namely, (i) a fast variational ansatz to optimize local Hamiltonians over symmetric states, (ii) a method to optimize symmetric, few-body Bell operators over symmetric states and (iii) a set of sufficient conditions to determine which symmetric states cannot be self-tested from few-body observables. As a by-product of our findings, we also provide a generic, analytical correspondence between arbitrary superpositions of n-qubit Dicke states and translationally-invariant diagonal matrix product states of bond dimension n.

• All authors: Aloy, A.; Fadel, M.; Tura Brugués, J.
• Date: 2021-03-01
• Journal: New Journal of Physics
• Volume: 23
• Issue: 3
• DOI: doi:10.1088/1367-2630/abe15e