Unbounded-Error One-Way Classical and Quantum Communication Complexity

This paper studies the gap between classical one-way communication complexity C(f) and its quantum counterpart Q(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 exactly (without an error of even ±1) one half as large as the latter. The result has an application to obtaining (again 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

• Type: Conference
• Year: 2007
• Where: ICALP
• Authors: Kazuo Iwama, Harumichi Nishimura, Rudy Raymond, Shigeru Yamashita
• Keywords: Boolean Function F, Classical One-way Communication, ICALP 2007, Success Probability, Theoretical Computer Science