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Quantum and Classical Communication-Space Tradeoffs from Rectangle Bounds

(Extended Abstract)
  • Hartmut Klauck
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3328)

Abstract

We derive lower bounds for tradeoffs between the communication C and space S for communicating circuits. The first such bound applies to quantum circuits. If for any problem f : X × YZ the multicolor discrepancy of the communication matrix of f  is 1/2 d , then any bounded error quantum protocol with space S, in which Alice receives some l  inputs, Bob r  inputs, and they compute f (x i ,y j ) for the l · r  pairs of inputs (x i ,y j ) needs communication C =Ω (lrd log | Z | /S). In particular, n × n-matrix multiplication over a finite field F requires C = Θ (n 3 log2 | F |/S), matrix-vector multiplication C= Θ (n 2 log2 | F |/S). We then turn to randomized bounded error protocols, and, utilizing a new direct product result for the one-sided rectangle lower bound on randomized communication complexity, derive the bounds C = Ω (n 3 /S 2) for Boolean matrix multiplication and C = Ω (n 2/S 2) for Boolean matrix-vector multiplication. These results imply a separation between quantum and randomized protocols when compared to quantum bounds in [KSW04] and partially answer a question by Beame et al.[BTY94].

Keywords

Hash Function Success Probability Communication Complexity Quantum Circuit Boolean Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Hartmut Klauck
    • 1
  1. 1.Institut für InformatikGoethe-Universität FrankfurtFrankfurt am MainGermany

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