dorsal/arxiv
View SchemaBound entanglement for continuous variables is a rare phenomenon
| Authors | Pawel Horodecki, J. Ignacio Cirac, Maciej Lewenstein |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103076 |
| URL | https://arxiv.org/abs/quant-ph/0103076 |
Abstract
We discuss the notion of bound entanglement (BE) for continuous variables (CV). We show that the set of non--distillable states (NDS) for CV is nowhere dense in the set of all states, i.e., the states of infinite--dimensional bipartite systems are generically distillable. This automatically implies that the sets of separable states, entangled states with positive partial transpose, and bound entangled states are also nowhere dense in the set of all states. All these properties significantly distinguish quantum CV systems from the spin like ones. The aspects of the definition of BE for CV is also analysed, especially in context of Schmidt numbers theory. In particular the main result is generalised by means of arbitrary Schmidt number and single copy regime.
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"abstract": "We discuss the notion of bound entanglement (BE) for continuous variables\n(CV). We show that the set of non--distillable states (NDS) for CV is nowhere\ndense in the set of all states, i.e., the states of infinite--dimensional\nbipartite systems are generically distillable. This automatically implies that\nthe sets of separable states, entangled states with positive partial transpose,\nand bound entangled states are also nowhere dense in the set of all states. All\nthese properties significantly distinguish quantum CV systems from the spin\nlike ones. The aspects of the definition of BE for CV is also analysed,\nespecially in context of Schmidt numbers theory. In particular the main result\nis generalised by means of arbitrary Schmidt number and single copy regime.",
"arxiv_id": "quant-ph/0103076",
"authors": [
"Pawel Horodecki",
"J. Ignacio Cirac",
"Maciej Lewenstein"
],
"categories": [
"quant-ph"
],
"title": "Bound entanglement for continuous variables is a rare phenomenon",
"url": "https://arxiv.org/abs/quant-ph/0103076"
},
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