dorsal/arxiv
View SchemaEntanglement of assistance and multipartite state distillation
| Authors | John A. Smolin, Frank Verstraete, Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505038 |
| URL | https://arxiv.org/abs/quant-ph/0505038 |
| DOI | 10.1103/PhysRevA.72.052317 |
| Journal | Phys. Rev. A, vol. 72, 052317, 2005 |
Abstract
We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal EPR pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and GHZ states; in fact, under a restricted class of protocols, which we call "one-way broadcasting", the GHZ-rate is shown to be optimal. This result implies a capacity theorem for quantum channels where the environment helps transmission by broadcasting the outcome of an optimally chosen measurement. We discuss generalisations to m parties, and show (for m=4) that the maximal amount of entanglement that can be localised between two parties is given by the smallest entropy of a group of parties of which the one party is a member, but not the other. This gives an explicit expression for the asymptotic localisable entanglement, and shows that any nontrivial ground state of a spin system can be used as a perfect quantum repeater if many copies are available in parallel. Finally, we provide evidence that any unital channel is asymptotically equivalent to a mixture of unitaries, and any general channel to a mixture of partial isometries.
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"abstract": "We find that the asymptotic entanglement of assistance of a general bipartite\nmixed state is equal to the smaller of its two local entropies. Our protocol\ngives rise to the asymptotically optimal EPR pair distillation procedure for a\ngiven tripartite pure state, and we show that it actually yields EPR and GHZ\nstates; in fact, under a restricted class of protocols, which we call \"one-way\nbroadcasting\", the GHZ-rate is shown to be optimal.\n This result implies a capacity theorem for quantum channels where the\nenvironment helps transmission by broadcasting the outcome of an optimally\nchosen measurement. We discuss generalisations to m parties, and show (for m=4)\nthat the maximal amount of entanglement that can be localised between two\nparties is given by the smallest entropy of a group of parties of which the one\nparty is a member, but not the other. This gives an explicit expression for the\nasymptotic localisable entanglement, and shows that any nontrivial ground state\nof a spin system can be used as a perfect quantum repeater if many copies are\navailable in parallel.\n Finally, we provide evidence that any unital channel is asymptotically\nequivalent to a mixture of unitaries, and any general channel to a mixture of\npartial isometries.",
"arxiv_id": "quant-ph/0505038",
"authors": [
"John A. Smolin",
"Frank Verstraete",
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.052317",
"journal_ref": "Phys. Rev. A, vol. 72, 052317, 2005",
"title": "Entanglement of assistance and multipartite state distillation",
"url": "https://arxiv.org/abs/quant-ph/0505038"
},
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