Quantum states with minimum phase uncertainty for the Süssmann measure
B. Daeubler, C. A. Miller, H. Risken, L. Schoendorff · Physica Scripta · 1993
We investigate those quantum states, which lead to minimum phase uncertainty for a fixed mean intensity. In contrast to the work of Bandilla, Paul, and Ritze (BPR) we employ instead of the usual variance measure for the phase the Süssmann measure. It turns out that our minimal states are of the form |ψ⟩ ∝ ∑ γ n | n ⟩. Because of this simple expression the phase distribution can be given analytically. It is shown that this distribution is about twice as peaked than the BPR phase minimum states. The Q-function is also obtained. It shows an asymmetry whereas the BPR states lead to a Q-function with a nearly symmetric ellipsoidal shape.