We consider two quantized harmonic oscillators and their phase-difference.
In our treatment, we use the phase-difference operator defined by Luis and
Sanchez-Soto [Phys. Rev. A, 1993, vol. 48, p. 4702]. A setup for direct mea
surement of the phase-difference is suggested, and its limitation discussed
. We also derive the phase-difference distributions for some states and com
pare the results to the single mode case. Finally, we consider the general
uncertainty relation for phase-difference and photon number-difference and
derive the two classes of minimum uncertainty states in the first manifold.