On continuous variable quantum algorithms for oracle identification problems

Details On continuous variable quantum algorithms for oracle identification problems On continuous variable quantum algorithms for oracle identification problems

2008-12-19

arxiv.org/abs/0812.3694v1

New Journal of Physics 11: 103035 (24 pp.), 21 October 2009

Physics

Quantum Physics

RevTeX4, 15 pages with 10 figures

Scientific paper

10.1088/1367-2630/11/10/103035

We establish a framework for oracle identification problems in the continuous variable setting, where the stated problem necessarily is the same as in the discrete variable case, and continuous variables are manifested through a continuous representation in an infinite-dimensional Hilbert space. We apply this formalism to the Deutsch-Jozsa problem and show that, due to an uncertainty relation between the continuous representation and its Fourier-transform dual representation, the corresponding Deutsch-Jozsa algorithm is probabilistic hence forbids an exponential speed-up, contrary to a previous claim in the literature.

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