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Near-Optimal Bounds on Bounded-Round Quantum Communication Complexity of Disjointness

Author(s): Braverman, Mark; Garg, A; Ko, YK; Mao, J; Touchette, D

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Abstract: We prove a near optimal round-communication trade off for the two-party quantum communication complexity of disjointness. For protocols with r rounds, we prove a lower bound of Ω(n/r) on the communication required for computing disjointness of input size n, which is optimal up to logarithmic factors. The previous best lower bound was Ω(n/r2) due to Jain, Radha krishnan and Sen. Along the way, we develop several tools for quantum information complexity, one of which is a lower bound for quantum information complexity in terms of the generalized discrepancy method. As a corollary, we get that the quantum communication complexity of any boolean function f is at most 2O(QIC(f)), where QIC(f) is the prior-free quantum information complexity of f (with error 1/3).
Publication Date: 17-Dec-2015
Electronic Publication Date: 2015
Citation: Braverman, M, Garg, A, Ko, YK, Mao, J, Touchette, D. (2015). Near-Optimal Bounds on Bounded-Round Quantum Communication Complexity of Disjointness. 2015-December (773 - 791. doi:10.1109/FOCS.2015.53
DOI: doi:10.1109/FOCS.2015.53
Pages: 773 - 791
Type of Material: Conference Article
Journal/Proceeding Title: Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Version: Author's manuscript

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