Cyclotomy and Ramanujan sums in quantum phase locking

Details Cyclotomy and Ramanujan sums in quantum phase locking Cyclotomy and Ramanujan sums in quantum phase locking

2003-04-14

arxiv.org/abs/quant-ph/0304101v2

Phys. Lett. A 315 (2003) 1-5

Physics

Quantum Physics

6 pages, 3 figures, version accepted at Phys. Lett. A

Scientific paper

10.1016/S0375-9601(03)00942-3

Phase-locking governs the phase noise in classical clocks through effects described in precise mathematical terms. We seek here a quantum counterpart of these effects by working in a finite Hilbert space. We use a coprimality condition to define phase-locked quantum states and the corresponding Pegg-Barnett type phase operator. Cyclotomic symmetries in matrix elements are revealed and related to Ramanujan sums in the theory of prime numbers. The employed mathematical procedures also emphasize the isomorphism between algebraic number theory and the theory of quantum entanglement

Affiliated with

Also associated with

No associations

Rating

Cyclotomy and Ramanujan sums in quantum phase locking does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cyclotomy and Ramanujan sums in quantum phase locking, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cyclotomy and Ramanujan sums in quantum phase locking will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-548137