Although the positive P representation (PPR) is widely used in the literature, there are still many open questions concerning its use as a general tool for solving problems in quantum optics. Recently, there has even been doubt as to whether it gives correct results at all. We present two nonlinear examples in which a comparison with independent methods shows the validity of the PPR. Then we show that, in general, the PPR is not restricted to a lower-dimensional subspace. Finally, we address the problem of initial conditions, which have to be chosen carefully to avoid incorrect results. More specifically, we show that the explicit form of the PPR that was given in the original existence proof leads to unphysical behavior when used as an initial distribution.

• Received 13 August 1990

DOI:https://doi.org/10.1103/PhysRevA.44.682