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Improved Quantum Communication Complexity Bounds for Disjointness and Equality

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STACS 2002 (STACS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2285))

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Abstract

We prove new bounds on the quantum communication complexity of the disjointness and equality problems. For the case of exact and non-deterministic protocols we show that these complexities are all equal to n+1, the previous best lower bound being n/2. We show this by improving a general bound for non-deterministic protocols of deWolf.We also give an O(√n·c log*n)-qubit bounded-error protocol for disjointness, modifying and improving the earlier O(√nlogn) protocol of Buhrman, Cleve, and Wigderson, and prove an ω(√n) lower bound for a class of protocols that includes the BCW-protocol as well as our new protocol.

Supported in part by Canada’s NSERC and the Pacific Institute for the Mathematical Sciences.

Supported by Talent grant S 62-565 from the Netherlands Organization for Scientific Research. Work conducted while at CWI, Amsterdam, partially supported by EU fifth framework project QAIP, IST-1999-11234.

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Author information

Authors and Affiliations

  1. Dept. of Comp. Sci., Univ. of Calgary, AB, Canada

    Peter Høyer

  2. UC Berkeley, 583 Soda Hall, 94720, Berkeley, CA, USA

    Ronald de Wolf

Authors
  1. Peter Høyer
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  2. Ronald de Wolf
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Editor information

Editors and Affiliations

  1. Institute for Computer Science, Free University of Berlin, Takustraße 9, 14195, Berlin, Germany

    Helmut Alt

  2. CNRS - I3S - INRIA Sophia Antipolis, 2004 Route des Lucioles, 06902, Sophia Antipolis, France

    Afonso Ferreira

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© 2002 Springer-Verlag Berlin Heidelberg

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Høyer, P., de Wolf, R. (2002). Improved Quantum Communication Complexity Bounds for Disjointness and Equality. In: Alt, H., Ferreira, A. (eds) STACS 2002. STACS 2002. Lecture Notes in Computer Science, vol 2285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45841-7_24

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  • DOI: https://doi.org/10.1007/3-540-45841-7_24

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  • Print ISBN: 978-3-540-43283-8

  • Online ISBN: 978-3-540-45841-8

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