Unbounded-Error One-Way Classical and Quantum Communication Complexity

  • Kazuo Iwama
  • Harumichi Nishimura
  • Rudy Raymond
  • Shigeru Yamashita
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)


This paper studies the gap between quantum one-way communication complexity Q(f) and its classical counterpart C(f), under the unbounded-error setting, i.e., it is enough that the success probability is strictly greater than 1/2. It is proved that for any (total or partial) Boolean function f, Q(f) = ⌈C(f)/2 ⌉, i.e., the former is always exactly one half as large as the latter. The result has an application to obtaining an exact bound for the existence of (m,n,p)-QRAC which is the n-qubit random access coding that can recover any one of m original bits with success probability ≥ p. We can prove that (m,n, > 1/2)-QRAC exists if and only if m ≤ 22n − 1. Previously, only the non-existence of (22n ,n, > 1/2)-QRAC was known.


Quantum State Boolean Function Success Probability Communication Complexity Classical Counterpart 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Kazuo Iwama
    • 1
  • Harumichi Nishimura
    • 2
  • Rudy Raymond
    • 3
  • Shigeru Yamashita
    • 4
  1. 1.School of Informatics, Kyoto University, Kyoto 606-8501, Sakyo-ku, Yoshida-HonmachiJapan
  2. 2.School of Science, Osaka Prefecture University, Sakai 599-8531, Gakuen-choJapan
  3. 3.Tokyo Research Laboratory, IBM Japan, Yamato 242-8502, Simotsuruma 1623-14Japan
  4. 4.Graduate School of Information Science, Nara Institute of Science and Technology, Nara 630-0192, Ikoma, Takayama-cho 8916-5Japan

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