Communication cost of entanglement transformations

P Hayden, AJ Winter

Research output: Contribution to journalArticle (Academic Journal)peer-review


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).
Translated title of the contributionCommunication cost of entanglement transformations
Original languageEnglish
Article numberArt no 012326
JournalPhysical Review A: Atomic, Molecular and Optical Physics
Volume67 (1)
Publication statusPublished - Jan 2003

Bibliographical note

Publisher: American Physical Soc
Other identifier: IDS Number: 642KY


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