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Volume 2 (2006) Article 1 pp. 1-18
All Quantum Adversary Methods are Equivalent
Received: August 4, 2005
Published: January 31, 2006
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Keywords: Quantum computing, query complexity, adversary lower bounds
ACM Classification: F.1.2, F.1.3
AMS Classification: 81P68, 68Q17

Abstract: [Plain Text Version]

The quantum adversary method is one of the most versatile lower-bound methods for quantum algorithms. We show that all known variants of this method are equivalent: spectral adversary (Barnum, Saks, and Szegedy, 2003), weighted adversary (Ambainis, 2003), strong weighted adversary (Zhang, 2005), and the Kolmogorov complexity adversary (Laplante and Magniez, 2004). We also present a few new equivalent formulations of the method. This shows that there is essentially one quantum adversary method. From our approach, all known limitations of these versions of the quantum adversary method easily follow.