Quantum conditional query complexity
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Peer-reviewed
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Article
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Abstract
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain highly efficient quantum algorithms for identity testing, equivalence testing and uniformity testing of probability distributions; (b) study the power of these oracles for testing properties of boolean functions, and obtain an algorithm for checking whether an n-input m-output boolean function is balanced or ϵ-far from balanced; and (c) give an algorithm, requiring Õ(n/ϵ) queries, for testing whether an n-dimensional quantum state is maximally mixed or not.
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Keywords
quantum query complexity, boolean functions, quantum oracle, quantum spectrum testing
Journal Title
Quantum Information and Computation
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Journal ISSN
1533-7146
Volume Title
17
Publisher
Rinton Press
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Sponsorship
EPSRC (1196264)
I.S.B.S. thanks EPSRC for financial support. S.S. acknowledges the support of Sidney Sussex College.