GAUSSIAN DENSITY-MATRICES - QUANTUM ANALOGS OF CLASSICAL STATES

We study quantum analogs of classical situations, i.e. quantum states possessing some specific classical attribute(s). These states seem qui te generally, to have the form of gaussian density matrices. Such stat es can always be parametrized as thermal squeezed states (TSS). We con sider the following specific cases: (a) Two beams that are built from initial beams which passed through a beam splitter cannot, classically , be distinguished from (appropriately prepared) two independent beams that did not go through a splitter. The only quantum states possessin g this classical attribute are TSS. (b) The classical Cramer's theorem was shown to have a quantum version (Hegerfeldt). Again, the states h ere are Gaussian density matrices. (c) The special case in the study o f the quantum version of Cramer's theorem, viz. when the state obtaine d after partial tracing is a pure state, leads to the conclusion that all states involved are zero temperature limit TSS. The classical anal og here are gaussians of zero width, i.e. all distributions are delta functions in phase space.