Work

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

Year: 2021

Type: article

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 .

Source: New Journal of Physics

DOI: 10.1088/1367-2630/abe15e

Authors: Albert Aloy, Matteo Fadel, Jordi Tura

Institutions: Institute of Photonic Sciences, Barcelona Institute of Science and Technology, University of Basel, Leiden University, Max Planck Institute of Quantum Optics

Language: English

Topic: Quantum Information and Cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,195