Unbounded-Error One-Way Classical and Quantum Communication Complexity
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- 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
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.
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