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

2019Journal article Restricted access
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dc.contributor.authorC.Dias, Nuno.
dc.contributor.authorde Grosson, M.
dc.contributor.authorN.Prata, João.
dc.date.accessioned2025-03-26T15:44:11Z
dc.date.available2025-03-26T15:44:11Z
dc.date.issued2019
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. (2019). A refinement of the Robertson–Schrödinger uncertainty principle and a Hirschman–Shannon inequality for Wigner distributions. Journal of Fourier Analysis and Applications, 25(1), 210-241
dc.identifier.doihttps://doi.org/10.1007/s00041-018-9602-xpt_PT
dc.identifier.urihttp://hdl.handle.net/10400.26/57457
dc.language.isoengpt_PT
dc.peerreviewedyes
dc.rights.urihttp://creativecommons.org/licenses/by-nc
dc.subjectWigner distribution
dc.subjectUncertainty principles
dc.subjectEntropic relations
dc.titleA refinement of the RobertsonSchrodinger 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.titleJournal of Fourier Analysis and Applicationspt_PT
oaire.versionhttp://purl.org/coar/version/c_970fb48d4fbd8a85
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT

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