Complete criterion for convex-Gaussian-state detection

Anna Vershynina
Phys. Rev. A 90, 062329 – Published 19 December 2014

Abstract

We present a criterion that determines whether a fermionic state is a convex combination of pure Gaussian states. This criterion is complete and characterizes the set of convex-Gaussian states from the inside. If a state passes a program it is a convex-Gaussian state and any convex-Gaussian state can be approximated with arbitrary precision by states passing the criterion. The criterion is presented in the form of a sequence of solvable semidefinite programs. It is also complementary to the one developed by de Melo, Ćwikliński, and Terhal, which aims at characterizing the set of convex-Gaussian states from the outside. Here we present an explicit proof that criterion by de Melo et al. is complete by estimating a distance between an n-extendible state, a state that passes the criterion, to the set of convex-Gaussian states.

  • Received 9 October 2014

DOI:https://doi.org/10.1103/PhysRevA.90.062329

©2014 American Physical Society

Authors & Affiliations

Anna Vershynina*

  • Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany

  • *annavershynina@gmail.com

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Issue

Vol. 90, Iss. 6 — December 2014

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