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Communication cost of entanglement transformations

Hayden, Patrick and Winter, Andreas (2003) Communication cost of entanglement transformations. Physical Review A, 67 (1). Art. No. 012326. ISSN 1050-2947. doi:10.1103/PhysRevA.67.012326.

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We study the amount of communication needed for two parties to transform some given joint pure state into another one, either exactly or with some fidelity. Specifically, we present a method to lower bound this communication cost even when the amount of entanglement does not increase. Moreover, the bound applies even if the initial state is supplemented with unlimited entanglement in the form of EPR (Einstein-Podolsky-Rosen) pairs and the communication is allowed to be quantum mechanical. We then apply the method to the determination of the communication cost of asymptotic entanglement concentration and dilution. While concentration is known to require no communication whatsoever, the best known protocol for dilution, discovered by H.-K. Lo and S. Popescu [Phys. Rev. Lett. 83, 1459 (1999)], requires exchange of a number of bits that is of the order of the square root of the number of EPR pairs. Here we prove a matching lower bound of the same asymptotic order, demonstrating the optimality of the Lo-Popescu protocol up to a constant factor and establishing the existence of a fundamental asymmetry between the concentration and dilution tasks. We also discuss states for which the minimal communication cost is proportional to their entanglement, such as the states recently introduced in the context of "embezzling entanglement" (W. van Dam and P. Hayden, e-print quant-ph/0201041).

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Additional Information:©2003 The American Physical Society (Received 16 April 2002; published 31 January 2003) We thank Wim van Dam for his suggestion to also consider general Rényi entropies, and Karol and Michał Horodecki for posing the problem solved in Remark 2. We want to thank Aram Harrow and Hoi-Kwong Lo for making their draft of [26] available to us and for stimulating discussions. P.H. was supported by National Science Foundation Grant No. EIA-0086038 and a grant from the Sherman Fairchild Foundation. A.W. is supported by the U.K. Engineering and Physical Sciences Research Council. This work was carried out during the second author’s visit to the Institute of Quantum Information, Caltech.
Subject Keywords:EPR paradox; quantum entanglement; quantum communication
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Record Number:CaltechAUTHORS:HAYpra03
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4512
Deposited By: Archive Administrator
Deposited On:25 Aug 2006
Last Modified:08 Nov 2021 20:17

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