Quantized Phase-Difference

From the experimentalist’ spoint of view, it is natural to think of aphase measurement as a measurement that involves a reference time. As a part of the system, the reference time generating “clock” must be taken into account in the quantum treatment of the measuring process. This could be argued to be the reason why there does not exist any observable corresponding to the absolute phase in the unrestricted Hilbert space.Luis and Sanchez-Soto [Phys. Rev. A 48, 4702 (1993)] have investigated the case where the “clock” is another harmonic oscillator and defined a Hermitian phase-difference operator, which is valid in the infinite Hilbert space.