The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing. (15th March 2021)

• Record Type: Journal Article
• Authors: Aloy, Albert; Fadel, Matteo; Tura, Jordi
• Is Part Of: New journal of physics. Volume 23:Number 3(2021)
• Publication Date: 2021-03-15
• Subjects: quantum marginal problem -- symmetric states -- variational optimization; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/abe15e
• Languages: English
• ISSNs: 1367-2630

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 .