De Gosson, Maurice;Luef, Franz

Remarks on the fact that the Uncertainty Principle does not determine the Quantum State

Phys. Lett., A No.364 (2007) p.453–457, Zbl:1203.81012, MR2307863


We discuss the relation between density matrices and the uncertainty
principle; this allows us to justify and explain a recent statement by
Man'ko textit{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
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