Exponential separation of quantum and classical one-way communication complexity

Exponential separation of quantum and classical one-way communication complexity

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by Ziv Bar-yossef , T. S. Jayram , Iordanis Kerenidis

Venue:	SIAM J. Comput
Citations:	29 - 1 self

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Datum	Value	Source
TITLE	Exponential separation of quantum and classical one-way communication complexity	INFERENCE
AUTHOR NAME	Ziv Bar-yossef	SVM HeaderParse 0.2
AUTHOR NAME	T. S. Jayram	SVM HeaderParse 0.2
AUTHOR NAME	Iordanis Kerenidis	SVM HeaderParse 0.2
ABSTRACT	Abstract. We give the first exponential separation between quantum and bounded-error randomized one-way communication complexity. Specifically, we define the Hidden Matching Problem HMn: 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 = xi ⊕ xj. We prove that the quantum one-way communication complexity of HMn 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 HMn, 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. Key words. Communication complexity, quantum computation, separation, hidden matching AMS subject classifications. 68P30,68Q15,68Q17,81P68 1. Introduction. The	SVM HeaderParse 0.2
VENUE	SIAM J. Comput	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
CITATIONS	25 found	ParsCit 1.0