International Colloquium on Automata, Languages, and Programming

ICALP 2007: Automata, Languages and Programming pp 110-121

Unbounded-Error One-Way Classical and Quantum Communication Complexity

  • Kazuo Iwama
  • Harumichi Nishimura
  • Rudy Raymond
  • Shigeru Yamashita
Conference paper

DOI: 10.1007/978-3-540-73420-8_12

Volume 4596 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Iwama K., Nishimura H., Raymond R., Yamashita S. (2007) Unbounded-Error One-Way Classical and Quantum Communication Complexity. In: Arge L., Cachin C., Jurdziński T., Tarlecki A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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