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Unbounded-Error Classical and Quantum Communication Complexity

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Algorithms and Computation (ISAAC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4835))

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Abstract

Since the seminal work of Paturi and Simon [26,FOCS’84 & JCSS’86], the unbounded-error classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently, [14, ICALP’07] found that the unbounded-error quantum communication complexity in the one-way communication model can also be investigated using the arrangement, and showed that it is exactly (without a difference of even one qubit) half of the classical one-way communication complexity. In this paper, we extend the arrangement argument to the two-way and simultaneous message passing (SMP) models. As a result, we show similarly tight bounds of the unbounded-error two-way/one-way/SMP quantum/classical communication complexities for any partial/total Boolean function, implying that all of them are equivalent up to a multiplicative constant of four. Moreover, the arrangement argument is also used to show that the gap between weakly unbounded-error quantum and classical communication complexities is at most a factor of three.

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Authors and Affiliations

  1. School of Informatics, Kyoto University, Kyoto 606-8501, Japan

    Kazuo Iwama

  2. School of Science, Osaka Prefecture University, Sakai 599-8531, Japan

    Harumichi Nishimura

  3. Tokyo Research Laboratory, IBM Japan, Yamato 242-8502, Japan

    Rudy Raymond

  4. Graduate School of Information Science, Nara Institute of Science and Technology, Ikoma 630-0192, Japan

    Shigeru Yamashita

Authors
  1. Kazuo Iwama
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  2. Harumichi Nishimura
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  3. Rudy Raymond
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  4. Shigeru Yamashita
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Editor information

Takeshi Tokuyama

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Iwama, K., Nishimura, H., Raymond, R., Yamashita, S. (2007). Unbounded-Error Classical and Quantum Communication Complexity. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_11

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  • DOI: https://doi.org/10.1007/978-3-540-77120-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77118-0

  • Online ISBN: 978-3-540-77120-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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