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

• URL: http://arxiv.org/abs/2001.04440v1
• Date: Mon, 13 Jan 2020 18:20:53 GMT
• Title: The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing
• Authors: Albert Aloy, Matteo Fadel, Jordi Tura
• Abstract summary: We present a method to solve the quantum marginal problem for symmetric $d$-level systems. We illustrate the applicability of the method in central quantum information problems with several exemplary case studies.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 determines 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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