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

Author(s): Braverman, Mark; Garg, Ankit; Ko, Young K; Mao, Jieming; Touchette, Dave

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Abstract: We prove a near optimal round-communication tradeoff for the two-party quantum communication complexity of disjointness. For protocols with r rounds, we prove a lower bound of Ω( ˜ n/r + 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 + r) due to Jain, Radhakrishnan and Sen [Proceedings of FOCS, 2003, pp. 220–229]. 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: 2018
Citation: Braverman, Mark, Ankit Garg, Young Kun Ko, Jieming Mao, and Dave Touchette. "Near-Optimal Bounds on the Bounded-Round Quantum Communication Complexity of Disjointness." SIAM Journal on Computing 47, no. 6 (2018): pp. 2277-2314. doi:10.1137/16M1061400
DOI: 10.1137/16M1061400
ISSN: 0097-5397
EISSN: 1095-7111
Pages: 2277 - 2314
Type of Material: Journal Article
Journal/Proceeding Title: SIAM Journal on Computing
Version: Author's manuscript

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