Phase distributions and large-amplitude states

We compare the properties of four quantum phase distributions: the London distribution, the integrated Wigner function, the integrated Q function, and the quadrature-based phase distribution. Their utility in determining the accuracy of phase-shift measurements and their transformation properties under rotations and squeezing transformations are considered. We show that two of the distributions become the same for large-amplitude states that are sufficiently localized in phase space. We call these states quasiclassical phase states. Large-amplitude classical states fall into this class. Some restrictions on how peaked phase distributions of classical states can be are discussed. For quasiclassical phase states, the phase distribution shares many of the properties of classical phase distributions and is measurable. For other states, such as small-amplitude or some nonclassical states, there is no phase distribution with all the desired properties.