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arXiv · 0706.3265

Unbounded-error One-way Classical and Quantum Communication Complexity

Kazuo Iwama·Harumichi Nishimura·Rudy Raymond·Shigeru Yamashita
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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 {\em unbounded-error} setting, i.e., it is enough that the success probability is strictly greater than 1/2. It is proved that for {\em any} (total or partial) Boolean function $f$, $Q(f)=\lceil C(f)/2 \rceil$, i.e., the former is always exactly 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 $\geq p$. We can prove that $(m,n,>1/2)$-QRAC exists if and only if $m\leq 2^{2n}-1$. Previously, only the construction of QRAC using one qubit, the existence of $(O(n),n,>1/2)$-RAC, and the non-existence of $(2^{2n},n,>1/2)$-QRAC were known.

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Kazuo Iwama, Harumichi Nishimura, Rudy Raymond, Shigeru Yamashita. 2007-06-22. Unbounded-error One-way Classical and Quantum Communication Complexity. https://doi.org/10.1007/978-3-540-73420-8_12

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