dorsal/arxiv
View SchemaBipartite and Multipartite Entanglement of Gaussian States
| Authors | Gerardo Adesso, Fabrizio Illuminati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510052 |
| URL | https://arxiv.org/abs/quant-ph/0510052 |
Abstract
In this chapter we review the characterization of entanglement in Gaussian states of continuous variable systems. For two-mode Gaussian states, we discuss how their bipartite entanglement can be accurately quantified in terms of the global and local amounts of mixedness, and efficiently estimated by direct measurements of the associated purities. For multimode Gaussian states endowed with local symmetry with respect to a given bipartition, we show how the multimode block entanglement can be completely and reversibly localized onto a single pair of modes by local, unitary operations. We then analyze the distribution of entanglement among multiple parties in multimode Gaussian states. We introduce the continuous-variable tangle to quantify entanglement sharing in Gaussian states and we prove that it satisfies the Coffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure, symmetric three-mode Gaussian states, at variance with their discrete-variable counterparts, allow a promiscuous sharing of quantum correlations, exhibiting both maximum tripartite residual entanglement and maximum couplewise entanglement between any pair of modes. Finally, we investigate the connection between multipartite entanglement and the optimal fidelity in a continuous-variable quantum teleportation network. We show how the fidelity can be maximized in terms of the best preparation of the shared entangled resources and, viceversa, that this optimal fidelity provides a clearcut operational interpretation of several measures of bipartite and multipartite entanglement, including the entanglement of formation, the localizable entanglement, and the continuous-variable tangle.
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"abstract": "In this chapter we review the characterization of entanglement in Gaussian\nstates of continuous variable systems. For two-mode Gaussian states, we discuss\nhow their bipartite entanglement can be accurately quantified in terms of the\nglobal and local amounts of mixedness, and efficiently estimated by direct\nmeasurements of the associated purities. For multimode Gaussian states endowed\nwith local symmetry with respect to a given bipartition, we show how the\nmultimode block entanglement can be completely and reversibly localized onto a\nsingle pair of modes by local, unitary operations. We then analyze the\ndistribution of entanglement among multiple parties in multimode Gaussian\nstates. We introduce the continuous-variable tangle to quantify entanglement\nsharing in Gaussian states and we prove that it satisfies the\nCoffman-Kundu-Wootters monogamy inequality. Nevertheless, we show that pure,\nsymmetric three-mode Gaussian states, at variance with their discrete-variable\ncounterparts, allow a promiscuous sharing of quantum correlations, exhibiting\nboth maximum tripartite residual entanglement and maximum couplewise\nentanglement between any pair of modes. Finally, we investigate the connection\nbetween multipartite entanglement and the optimal fidelity in a\ncontinuous-variable quantum teleportation network. We show how the fidelity can\nbe maximized in terms of the best preparation of the shared entangled resources\nand, viceversa, that this optimal fidelity provides a clearcut operational\ninterpretation of several measures of bipartite and multipartite entanglement,\nincluding the entanglement of formation, the localizable entanglement, and the\ncontinuous-variable tangle.",
"arxiv_id": "quant-ph/0510052",
"authors": [
"Gerardo Adesso",
"Fabrizio Illuminati"
],
"categories": [
"quant-ph",
"cond-mat.other",
"math-ph",
"math.MP",
"physics.optics"
],
"title": "Bipartite and Multipartite Entanglement of Gaussian States",
"url": "https://arxiv.org/abs/quant-ph/0510052"
},
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