The hyperbolic, the arithmetic and the quantum phase

Michel Planat, Haret Rosu
2004 Journal of Optics B-Quantum and Semiclassical Optics  
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
more » ... or Kloosterman pairs of phase-locked states is introduced.
doi:10.1088/1464-4266/6/6/018 fatcat:wuk2co3yjfdvtldxosibdly6ry