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Lower Bounds on the Deterministic and Quantum Communication Complexity of Hamming-Distance Problems

Published: 26 June 2015 Publication History

Abstract

Alice and Bob want to know if two strings of length n are almost equal. That is, do the strings differ on at most a bits? Let 0 ⩽ an − 1. We show (1) any deterministic protocol—as well as any error-free quantum protocol (C* version)—for this problem requires at least n − 2 bits of communication, and (2) a lower bound of n/2 − 1 for error-free Q* quantum protocols. We also show the same results for determining if two strings differ in exactly a bits. Our results are obtained by lower-bounding the ranks of the appropriate matrices.

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  1. Lower Bounds on the Deterministic and Quantum Communication Complexity of Hamming-Distance Problems

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    cover image ACM Transactions on Computation Theory
    ACM Transactions on Computation Theory  Volume 7, Issue 3
    July 2015
    83 pages
    ISSN:1942-3454
    EISSN:1942-3462
    DOI:10.1145/2798085
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Association for Computing Machinery

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    Publication History

    Published: 26 June 2015
    Accepted: 01 December 2014
    Revised: 01 August 2014
    Received: 01 November 2012
    Published in TOCT Volume 7, Issue 3

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    Author Tags

    1. Communication complexity
    2. Hamming distance

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    • (2018)Analysis of Solar Irradiation Time Series Complexity and Predictability by Combining Kolmogorov Measures and Hamming Distance for La Reunion (France)Entropy10.3390/e2008057020:8(570)Online publication date: 1-Aug-2018
    • (2018)Near Log-Convexity of Measured Heat in (Discrete) Time and Consequences2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2018.00095(967-978)Online publication date: Oct-2018

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