Quantum conditional query complexity
Quantum Information and Computation
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Sardharwalla, I., Strelchuk, S., & Jozsa, R. (2017). Quantum conditional query complexity. Quantum Information and Computation, 17 (7-8), 541-567. http://www.rintonpress.com/journals/qicabstracts/qicabstracts17-78.html
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.
quantum query complexity, boolean functions, quantum oracle, quantum spectrum testing
I.S.B.S. thanks EPSRC for financial support. S.S. acknowledges the support of Sidney Sussex College.
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This record's URL: https://www.repository.cam.ac.uk/handle/1810/266286