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A refinement of the Robertson-Schrodinger uncertainty principle and a Hirschman-Shannon inequality for Wigner distributions

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dc.contributor.authorDias, Nuno Costa
dc.contributor.authorde Gosson, M.
dc.contributor.authorPrata, João Nuno
dc.date.accessioned2025-02-07T15:22:27Z
dc.date.available2025-02-07T15:22:27Z
dc.date.issued2017
dc.description.abstractWe propose a refinement of the Robertson–Schrödinger uncertainty principle (RSUP) using Wigner distributions. This new principle is stronger than the RSUP. In particular, and unlike the RSUP, which can be saturated by many phase space functions, the refined RSUP can be saturated by pure Gaussian Wigner functions only. Moreover, the new principle is technically as simple as the standard RSUP. In addition, it makes a direct connection with modern harmonic analysis, since it involves the Wigner transform and its symplectic Fourier transform, which is the radar ambiguity function. As a by-product of the refined RSUP, we derive inequalities involving the entropy and the covariance matrix of Wigner distributions. These inequalities refine the Shanon and the Hirschman inequalities for the Wigner distribution of a mixed quantum state. We prove sharp estimates which critically depend on the purity of and which are saturated in the Gaussian case.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationDias, N.C., de Gosson, M.A. & Prata, J.N. A Refinement of the Robertson–Schrödinger Uncertainty Principle and a Hirschman–Shannon Inequality for Wigner Distributions. J Fourier Anal Appl 25, 210–241 (2019).pt_PT
dc.identifier.doihttps://doi.org/10.48550/arXiv.1712.09475pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.26/54305
dc.language.isoengpt_PT
dc.titleA refinement of the Robertson-Schrodinger uncertainty principle and a Hirschman-Shannon inequality for Wigner distributionspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage241pt_PT
oaire.citation.startPage210pt_PT
oaire.citation.titleFourier Analysis and Applications.pt_PT
oaire.citation.volume25pt_PT
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT

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