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29 March 2024
 
  » arxiv » quant-ph/0505038

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Entanglement of assistance and multipartite state distillation
John A. Smolin ; Frank Verstraete ; Andreas Winter ;
Date 6 May 2005
Subject quant-ph
AbstractWe 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.
Source arXiv, quant-ph/0505038
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