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arXiv · 1203.5201

Mutually unbiased bases for the rotor degree of freedom

Xin Lü·Philippe Raynal·Berthold-Georg Englert
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Abstract

We consider the existence of a continuous set of mutually unbiased bases for the continuous and periodic degree of freedom that describes motion on a circle (rotor degree of freedom). By a singular mapping of the circle to the line, we find a first, but somewhat unsatisfactory, continuous set which does not relate to an underlying Heisenberg pair of complementary observables. Then, by a nonsingular mapping of the discrete angular momentum basis of the rotor onto the Fock basis for linear motion, we construct such a Heisenberg pair for the rotor and use it to obtain a second, fully satisfactory, set of mutually unbiased bases.

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Xin Lü, Philippe Raynal, Berthold-Georg Englert. 2012-03-23. Mutually unbiased bases for the rotor degree of freedom. https://arxiv.org/abs/1203.5201

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