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

New Journal of Physics, vol. 23, pp. 033026

Abstract

Abstract 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 .

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