The uncertainty principle and positivity of trace-class operators: applications to density operators (Q2427382)

From the paper: The authors discuss a necessary (but generally not sufficient) condition for a selfadjoint trace-class operator to be positive. This allows to state a relation between density operators and the notion of symplectic quantum cell introduced in a previous work. Hardy's uncertainty principle is applied to Gaussian estimates for the Wigner distribution. This allows to recover in a very simple way the fact that the Wigner transform of a square integrable function cannot have compact support.