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Symplectic invariants, entropic measures and correlations of Gaussian states
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Symplectic invariants, entropic measures and correlations of Gaussian states
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We present a derivation of the Von Neumann entropy and mutual information of arbitrary two--mode Gaussian states, 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 (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different hierarchies of mixed 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 the correlations present in a generic state.
Forward citations
Cited by 2 Pith papers
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Hidden quantum-informatic symmetries of quasi-de Sitter backgrounds
Wands-dual quasi-de Sitter backgrounds produce identical symplectic eigenvalues in the Gaussian covariance matrix of localized scalar modes, revealing a quantum-informatic symmetry preserved by the duality's canonical...
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On generalization of Williamson's theorem to real symmetric matrices
Generalizes Williamson's theorem to real symmetric matrices allowing arbitrary real symplectic eigenvalues, with explicit constructions and perturbation bounds for the class EigSpSm(2n).
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