Inseparability criteria based on matrices of moments

Adam Miranowicz, Marco Piani, Paweł Horodecki, and Ryszard Horodecki
Phys. Rev. A 80, 052303 – Published 3 November 2009

Abstract

Inseparability criteria for continuous and discrete bipartite quantum states based on moments of annihilation and creation operators are studied by developing the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. 95, 230502 (2005)]. If a state is separable, then the corresponding matrix of moments is separable too. Thus, we derive generalized criteria based on the separability properties of the matrix of moments. In particular, a criterion based on realignment of moments in the matrix is proposed as an analog of the standard realignment criterion for density matrices. Other inseparability inequalities are obtained by applying positive maps to the matrix of moments. Usefulness of the Shchukin-Vogel criterion to describe bipartite-entanglement of more than two modes is demonstrated: we obtain various three-mode inseparability criteria, including some previously known ones, which were originally derived from the Cauchy-Schwarz inequality.

  • Received 17 July 2009

DOI:https://doi.org/10.1103/PhysRevA.80.052303

©2009 American Physical Society

Authors & Affiliations

Adam Miranowicz1,2, Marco Piani1,3, Paweł Horodecki4,5, and Ryszard Horodecki1,5

  • 1Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland
  • 2Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
  • 3Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada
  • 4Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80-952 Gdańsk, Poland
  • 5National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland

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Issue

Vol. 80, Iss. 5 — November 2009

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