Quantum Entanglement and the Communication Complexity of the Inner Product Function

Details Quantum Entanglement and the Communication Complexity of the Inner Product Function Quantum Entanglement and the Communication Complexity of the Inner Product Function

1997-08-11

arxiv.org/abs/quant-ph/9708019v3

Lect.Notes Comput.Sci. 1509 (1998) 61-74

Physics

Quantum Physics

14 pages, LaTeX w/ llncs style, no figures, made changes in notation in order to be consistent with other papers. To appear in

Scientific paper

We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for both exact protocols, as well as for protocols that determine the answer with bounded-error probability. Our proofs employ a novel kind of "quantum" reduction from a quantum information theory problem to the problem of computing the inner product. The communication required for the former problem can then be bounded by an application of Holevo's theorem. We also give a specific example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit.

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