The quantum phase problem and the linear phase insensitive quantum amplifier

We establish a general condition which must be obeyed by every operator referred to the quantum phase. This condition is derived on the basis of the model of the linear phase insensitive amplifier, proposed by Glauber. We demonstrate that the phase operators, most frequently discussed in literature, do not satisfy this condition, and that no Hermitian phase operator can satisfy this condition. We also show by explicit construction that this condition singles out one particular probability operator measure as the only candidate for the correct definition of the phase distribution of the quantum states.