Classical Communication Cost in Distributed Quantum Information Processing - A generalization of Quantum Communication Complexity

Abstract

We study the amount of classical communication needed for distributed quantum information processing. In particular, we introduce the concept of "remote preparation" of a quantum state. Given an ensemble of states, Alice's task is to help Bob in a distant laboratory to prepare a state of her choice. We find several examples of an ensemble with an entropy S where the remote preparation can be done with a communication cost lower than the amount (2S) required by standard teleportation. We conjecture that, for an arbitrary N-dimensional pure state, its remote preparation requires 2log_2 N bits of classical communication, as in standard teleportation.

Revised Version. Accepted on March 31 for publication in Physical Review A. Proof of Theorem 3 clarified. A Proviso added to the statement of Conjecture 4. Related results on randomization and private quantum channel noted

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