Extremal entanglement and mixedness in continuous variable systems
Abstract
We investigate extremal entanglement for Gaussian states of continuous variable systems. We introduce generalized entropies based on p-norms to quantify mixedness, and give their explicit expression in terms of symplectic spectra. We compare the hierarchies of mixedness provided by such measures with the one provided by the purity for n-mode states. We then review the argument proving the existence of both maximally and minimally entangled two--mode states at given global and marginal purities (with the entanglement quantified by the logarithmic negativity). Exploiting these results, we extend such an analysis to generalized entropies, fully characterizing maximally and minimally entangled states for given global and local generalized entropies. The privileged role of the purity in quantifying the mixedness of continuous variable systems is stressed and a proposal to estimate entanglement by purity measurements is finally reviewed.Keywords
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