Article

Exponential separation of quantum and classical one-way communication complexity

Authors:

Ziv Bar-Yossef,

Iordanis KerenidisAuthors Info & Claims

STOC '04: Proceedings of the thirty-sixth annual ACM symposium on Theory of computing

Pages 128 - 137

https://doi.org/10.1145/1007352.1007379

Published: 13 June 2004 Publication History

Abstract

We give the first exponential separation between quantum and bounded-error randomized one-way communication complexity. Specifically, we define the Hidden Matching Problem HM_n: Alice gets as input a string x ∈ (0, 1)ⁿ and Bob gets a perfect matching M on the n coordinates. Bob's goal is to output a tuple [i,j,b] such that the edge (i,j) belongs to the matching M and b = x_i ⊕ x_j. We prove that the quantum one-way communication complexity of HM_n is O(log n), yet any randomized one-way protocol with bounded error must use Ω(√n) bits of communication. No asymptotic gap for one-way communication was previously known. Our bounds also hold in the model of Simultaneous Messages (SM) and hence we provide the first exponential separation between quantum SM and randomized SM with public coins.For a Boolean decision version of HM_n, we show that the quantum one-way communication complexity remains O(log n) and that the 0-error randomized one-way communication complexity is Ω(n). We prove that any randomized linear one-way protocol with bounded error for this problem requires Ω(√[3] n log n) bits of communication.

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Exponential separation of quantum and classical one-way communication complexity

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cover image ACM Conferences

STOC '04: Proceedings of the thirty-sixth annual ACM symposium on Theory of computing

June 2004

660 pages

ISBN:1581138520

DOI:10.1145/1007352

Program Chair:
László Babai
University of Chicago, Chicago, IL

Copyright © 2004 ACM.

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Published: 13 June 2004

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Chen XCohen-Addad VJayaram RLevi AWaingarten ESaha BServedio R(2023)Streaming Euclidean MST to a Constant FactorProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585168(156-169)Online publication date: 2-Jun-2023
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