Quantum entanglement and the communication complexity of the inner product function (1998) [45 citations — 9 self]
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@INPROCEEDINGS{Cleve98quantumentanglement,author = {Richard Cleve and Michael Nielsen},
title = {Quantum entanglement and the communication complexity of the inner product function},
booktitle = {In Proceedings of 1st NASA QCQC conference, volume 1509 of Lecture Notes in Computer Science},
year = {1998},
pages = {61--74},
publisher = {Springer}
}
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Abstract:
Abstract. We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an apriorisupply 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. 1 Introduction and Summary of Results The communication complexity of a function f: {0, 1} n ×{0, 1} n →{0, 1} is defined as the minimum amount of communication necessary among two parties, conventionally referred to as Alice and Bob, in order for, say, Bob to acquire
