Quantum counterfeit coin problems

Authors:
Kazuo Iwama;Harumichi Nishimura;Rudy Raymond;Junichi Teruyama
Affiliations:
School of Informatics, Kyoto University, Yoshida-Honmachi, Kyoto 606-8501, Japan;Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan;IBM ResearchTokyo, 1623-14 Shimotsuruma, Yamato 242-8502, Japan;School of Informatics, Kyoto University, Yoshida-Honmachi, Kyoto 606-8501, Japan
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only ''balanced'' or ''tilted'' information and that we know the number k of false coins in advance. The balance scale can be modeled by a certain type of oracle and its query complexity is a measure for the cost of weighing algorithms (the number of weighings). In this paper, we study the quantum query complexity for this problem. Let Q(k,N) be the quantum query complexity of finding all k false coins from the N given coins. We show that for any k and N such that k