Remarks on the Fact that the Uncertainty Principle Does Not Determine the Quantum State

Abstract

We discuss the relation between density matrices and the uncertainty principle; this allows us to justify and explain a recent statement by Man'ko et al. We thereafter use Hardy's uncertainty principle to prove a new result for Wigner distributions dominated by a Gaussian and we relate this result to the coarse-graining of phase-space by "quantum blobs".

To appaer in Phys. Lett. A