The hyperbolic, the arithmetic and the quantum phase

Details The hyperbolic, the arithmetic and the quantum phase The hyperbolic, the arithmetic and the quantum phase

2003-09-09

arxiv.org/abs/math-ph/0309022v2

Journal of Optics B 6 (2004) S583

Physics

Mathematical Physics

accepted for publication for the special issue of J. Opt. B, in relation to ICSSUR, Puebla (Mexico): Foundations of Quantum Op

Scientific paper

10.1088/1464-4266/6/6/018

We develop a new approach of the quantum phase in an Hilbert space of finite dimension which is based on the relation between the physical concept of phase locking and mathematical concepts such as cyclotomy and the Ramanujan sums. As a result, phase variability looks quite similar to its classical counterpart, having peaks at dimensions equal to a power of a prime number. Squeezing of the phase noise is allowed for specific quantum states. The concept of phase entanglement for Kloosterman pairs of phase-locked states is introduced.

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