UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2024-11-22 2:24
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Conference: Bucharest University Faculty of Physics 2004 Meeting


Section: Statistical Physics and Quantum Mechanics Seminar


Title:
On the separability criterion for two-mode Gaussian states


Authors:
Paulina Marian (1) and Tudor A. Marian (2)


Affiliation:
(1) Department of Chemistry, University of Bucharest,

Blvd Regina Elisabeta 4-12, R-70346 Bucharest, Romania

(2) Department of Physics, University of Bucharest, P.O.Box MG-11, R-76900 Bucharest-Magurele, Romania


E-mail


Keywords:
two-mode Gaussian states,entanglement,EPR-inequalities


Abstract:
Recent developments in the theory of quantum information focused on a deeper understanding of the properties of the entangled states. Quantifying entanglement (inseparability) of bipartite mixed states is still an open problem for the majority of the quantum systems of experimental interest. However, in the important case of the two-mode Gaussian states of the radiation field a separability criterion was formulated in two different ways. Thus, Duan e. a. (Physical Review Letters 84, 2722 (2000)) developed a separability criterion based on a set of inequalities satisfied by the variances of an ingeniously defined pair of Einstein-Podolsky-Rosen (EPR)-like operators. At the same time, Simon (Physical Review Letters 84, 2726 (2000)) showed that the preservation of the non-negativity of the density matrix under partial transposition is also a sufficient condition for the separability of two-mode Gaussian states. Simons formulation is very elegant and displays the invariance of the entanglement properties under local unitary transformations. In this work we revisit the separability criterion in the formulation of Duan e. a. Our aim here is to establish the precise link between separability and one of the above-mentioned inequalities. We are thus able to find the EPR operators that allow us to probe separability of an arbitarary two-mode Gaussian state. Possible applications in evaluating the entanglement of formation for such states are then briefly discussed.