Symplectic invariants and entropic measures of Gaussian states

Preprint

4 August 2003

preprint
Published by arXiv in arXiv

Abstract

We present a derivation of the Von Neumann entropy and mutual information of an arbitrary bipartite Gaussian state, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity is determined by only one invariant, so that these two quantities yield two different hierarchies for the mixedness of Gaussian states. A comparison between mutual information and entanglement of formation for symmetric states is considered, remarking the crucial role of the symplectic eigenvalues in qualifying and quantifying correlations.

Keywords

SYMPLECTIC INVARIANTS
VON NEUMANN ENTROPY
MUTUAL INFORMATION
GAUSSIAN STATES
EIGENVALUES

All Related Versions

Version 1, 2003-07-10, ArXiv
Version 2, 2003-07-30, ArXiv
Version 3, 2003-08-04, ArXiv
Version 4, 2003-12-16, ArXiv
Published version: Journal of Physics B: Atomic, Molecular and Optical Physics, 37 (2), L21.

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