Extremal entanglement and mixedness in continuous variable systems

Journal Article · Sun Aug 01 04:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.022318· OSTI ID:20645863

Adesso, Gerardo; Serafini, Alessio; Illuminati, Fabrizio ^[1]

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1. Dipartimento di Fisica 'E. R. Caianiello', Universita di Salerno, INFM UdR di Salerno, INFN Sezione di Napoli, Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi, SA (Italy)

We investigate the relationship between mixedness and entanglement for Gaussian states of continuous variable systems. We introduce generalized entropies based on Schatten p norms to quantify the mixedness of a state and derive their explicit expressions in terms of symplectic spectra. We compare the hierarchies of mixedness provided by such measures with the one provided by the purity (defined as tr {rho}{sup 2} for the state {rho}) for generic n-mode states. We then review the analysis proving the existence of both maximally and minimally entangled states at given global and marginal purities, with the entanglement quantified by the logarithmic negativity. Based on these results, we extend such an analysis to generalized entropies, introducing and fully characterizing maximally and minimally entangled states for given global and local generalized entropies. We compare the different roles played by the purity and by the generalized p entropies in quantifying the entanglement and the mixedness of continuous variable systems. We introduce the concept of average logarithmic negativity, showing that it allows a reliable quantitative estimate of continuous variable entanglement by direct measurements of global and marginal generalized p entropies.

• OSTI ID: 20645863
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

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