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

Maurice de Gosson·Franz Luef
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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".

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Maurice de Gosson, Franz Luef. 2007-03-07. Remarks on the Fact that the Uncertainty Principle Does Not Determine the Quantum State. https://arxiv.org/abs/quant-ph/0703061

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