Unbounded-error one-way classical and quantum communication complexity

Authors:
Kazuo Iwama;Harumichi Nishimura;Rudy Raymond;Shigeru Yamashita
Affiliations:
School of Informatics, Kyoto University, Kyoto, Yoshida-Honmachi, Japan;School of Science, Osaka Prefecture University, Sakai, Gakuen-cho, Japan;Tokyo Research Laboratory, IBM Japan, Yamato, Japan;Graduate School of Information Science, Nara Institute of Science and Technology, Takayama-cho, Japan
Venue:
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Year:
2007

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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.