dorsal/arxiv
View SchemaExtremal entanglement and mixedness in continuous variable systems
| Authors | Gerardo Adesso, Alessio Serafini, Fabrizio Illuminati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402124 |
| URL | https://arxiv.org/abs/quant-ph/0402124 |
| DOI | 10.1103/PhysRevA.70.022318 |
| Journal | Phys.Rev. A70 (2004) 022318 |
Abstract
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 ${\rm tr} \varrho^2$ for the state $\varrho$) 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.
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"abstract": "We investigate the relationship between mixedness and entanglement for\nGaussian states of continuous variable systems. We introduce generalized\nentropies based on Schatten $p$-norms to quantify the mixedness of a state, and\nderive their explicit expressions in terms of symplectic spectra. We compare\nthe hierarchies of mixedness provided by such measures with the one provided by\nthe purity (defined as ${\\rm tr} \\varrho^2$ for the state $\\varrho$) for\ngeneric $n$-mode states. We then review the analysis proving the existence of\nboth maximally and minimally entangled states at given global and marginal\npurities, with the entanglement quantified by the logarithmic negativity. Based\non these results, we extend such an analysis to generalized entropies,\nintroducing and fully characterizing maximally and minimally entangled states\nfor given global and local generalized entropies. We compare the different\nroles played by the purity and by the generalized $p$-entropies in quantifying\nthe entanglement and the mixedness of continuous variable systems. We introduce\nthe concept of average logarithmic negativity, showing that it allows a\nreliable quantitative estimate of continuous variable entanglement by direct\nmeasurements of global and marginal generalized $p$-entropies.",
"arxiv_id": "quant-ph/0402124",
"authors": [
"Gerardo Adesso",
"Alessio Serafini",
"Fabrizio Illuminati"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"doi": "10.1103/PhysRevA.70.022318",
"journal_ref": "Phys.Rev. A70 (2004) 022318",
"title": "Extremal entanglement and mixedness in continuous variable systems",
"url": "https://arxiv.org/abs/quant-ph/0402124"
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