The relation between the scaling of Husimi functions and the linear phase insensitive amplification of the corresponding quantum states and its implications
Dragomir M Davidović, Dragutin Lalović · Journal of Physics A Mathematical and General · 1996
Using the description of the linear phase insensitive amplification of a quantum state available in the literature we prove that to every state , produced from the initial state by such amplification, there corresponds a phase space distribution , where is the Husimi function of the initial state. The scaling parameter satisfies the relation and decreases with time while, as we have shown earlier, the scaled function is again a Husimi distribution. We prove, using these facts, that if the definition of the phase insensitive amplification is physically correct then the distribution of the phase of a state is unambiguously given as the corresponding marginal distribution obtained from its Husimi distribution represented in polar coordinates.