Entangled symmetric states and copositive matrices

Quantum, vol. 5, pp. 561

Abstract

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For the simplest symmetric states, i.e., the diagonal symmetric (DS) states, it has been shown that there exists a correspondence between exceptional (non-exceptional) copositive matrices and non-decomposable (decomposable) Entanglement Witnesses (EWs). Here we show that EWs of symmetric, but not DS, states can also be constructed from extended copositive matrices, providing new examples of bound entangled symmetric states, together with their corresponding EWs, in arbitrary odd dimensions.

Authors 3

1. Carlo Marconi

   Universitat Autònoma de Barcelona

   Affiliation as printed

   Física Teòrica: Informació i Fenòmens Quàntics. Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

2. Albert Aloy

   Barcelona Institute of Science and Technology · Institute of Photonic Sciences

   Affiliation as printed

   ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

3. Jordi Tura Aachen Instituut-Lorentz

   Leiden University · Max Planck Institute of Quantum Optics

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

   Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany