Communication cost of entanglement transformations

Journal Article · Wed Jan 01 04:00:00 EST 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.67.012326· OSTI ID:20634104

Hayden, Patrick; Winter, Andreas ^[1]

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1. Institute for Quantum Information, Caltech 107-81, Pasadena, California 91125 (United States)

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)

• OSTI ID: 20634104
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 67; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ASYMMETRY
CORRELATIONS
DATA TRANSMISSION
ENERGY LEVELS
QUANTUM MECHANICS
TRANSFORMATIONS