dorsal/arxiv
View SchemaMultipartite entanglement in three-mode Gaussian states of continuous variable systems: Quantification, sharing structure and decoherence
| Authors | Gerardo Adesso, Alessio Serafini, Fabrizio Illuminati |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512124 |
| URL | https://arxiv.org/abs/quant-ph/0512124 |
| DOI | 10.1103/PhysRevA.73.032345 |
| Journal | Phys. Rev. A 73, 032345 (2006) |
Abstract
We present a complete analysis of multipartite entanglement of three-mode Gaussian states of continuous variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations will be quantified by a proper convex roof extension of the squared logarithmic negativity (the contangle), satisfying a monogamy relation for multimode Gaussian states, whose proof will be reviewed and elucidated. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communication and defines a measure of genuine tripartite entanglement. We analytically determine the residual contangle for arbitrary pure three-mode Gaussian states and study the distribution of quantum correlations for such states. This will lead us to show that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite residual entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/$W$ states of continuous variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the $W$ states of three qubits. We finally consider the action of decoherence on tripartite entangled Gaussian states, studying the decay of the residual contangle. The GHZ/$W$ states are shown to be maximally robust under both losses and thermal noise.
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"abstract": "We present a complete analysis of multipartite entanglement of three-mode\nGaussian states of continuous variable systems. We derive standard forms which\ncharacterize the covariance matrix of pure and mixed three-mode Gaussian states\nup to local unitary operations, showing that the local entropies of pure\nGaussian states are bound to fulfill a relationship which is stricter than the\ngeneral Araki-Lieb inequality. Quantum correlations will be quantified by a\nproper convex roof extension of the squared logarithmic negativity (the\ncontangle), satisfying a monogamy relation for multimode Gaussian states, whose\nproof will be reviewed and elucidated. The residual contangle, emerging from\nthe monogamy inequality, is an entanglement monotone under Gaussian local\noperations and classical communication and defines a measure of genuine\ntripartite entanglement. We analytically determine the residual contangle for\narbitrary pure three-mode Gaussian states and study the distribution of quantum\ncorrelations for such states. This will lead us to show that pure, symmetric\nstates allow for a promiscuous entanglement sharing, having both maximum\ntripartite residual entanglement and maximum couplewise entanglement between\nany pair of modes. We thus name these states GHZ/$W$ states of continuous\nvariable systems because they are simultaneous continuous-variable counterparts\nof both the GHZ and the $W$ states of three qubits. We finally consider the\naction of decoherence on tripartite entangled Gaussian states, studying the\ndecay of the residual contangle. The GHZ/$W$ states are shown to be maximally\nrobust under both losses and thermal noise.",
"arxiv_id": "quant-ph/0512124",
"authors": [
"Gerardo Adesso",
"Alessio Serafini",
"Fabrizio Illuminati"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"math-ph",
"math.MP",
"physics.optics"
],
"doi": "10.1103/PhysRevA.73.032345",
"journal_ref": "Phys. Rev. A 73, 032345 (2006)",
"title": "Multipartite entanglement in three-mode Gaussian states of continuous variable systems: Quantification, sharing structure and decoherence",
"url": "https://arxiv.org/abs/quant-ph/0512124"
},
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