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In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies. It turns out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. This is stronger than the usual statement of the uncertainty principle in terms of the product of standard deviations. In 1957, Hirschman considered a function f and its Fourier transform g such that where the "≈" indicates convergence in L2, and normalized so that (by Plancherel's theorem),

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rdfs:label	Entropic uncertainty (en)
rdfs:comment	In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies. It turns out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. This is stronger than the usual statement of the uncertainty principle in terms of the product of standard deviations. In 1957, Hirschman considered a function f and its Fourier transform g such that where the "≈" indicates convergence in L2, and normalized so that (by Plancherel's theorem), (en)
dcterms:subject	Information theory Quantum mechanical entropy Physical quantities Inequalities
Wikipage page ID	857780 (xsd:integer)
Wikipage revision ID	1097598481 (xsd:integer)
Link from a Wikipage to another Wikipage	Calculus of variations Riesz–Thorin theorem Uncertainty principle Variance Von Neumann entropy Inequalities in information theory Rényi entropy Phase space William Beckner (mathematician) Lebesgue measure Logarithmic Schrödinger equation Information theory Fourier analysis Fourier transform Quantum mechanical entropy Normal distribution Differential entropy Gaussian distribution Babenko–Beckner inequality Physical quantities Inequalities Bit Information theory Nat (unit) Isidore Isaac Hirschman, Jr. Plancherel theorem Normal probability distribution Hugh Everett Hermite functions
Link from a Wikipage to an external page	https://pure.uva.nl/ws/files/2210736/46650_28y.pdf https://arxiv.org/abs/math/0605510v1 https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.060104
sameAs	Entropic uncertainty Entropic uncertainty Entropic uncertainty Entropic uncertainty
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has abstract	In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies. It turns out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. This is stronger than the usual statement of the uncertainty principle in terms of the product of standard deviations. In 1957, Hirschman considered a function f and its Fourier transform g such that where the "≈" indicates convergence in L2, and normalized so that (by Plancherel's theorem), He showed that for any such functions the sum of the Shannon entropies is non-negative, A tighter bound, was conjectured by Hirschman and Everett, proven in 1975 by W. Beckner and in the same year interpreted as a generalized quantum mechanical uncertainty principle by Białynicki-Birula and Mycielski.The equality holds in the case of Gaussian distributions.Note, however, that the above entropic uncertainty function is distinctly different from the quantum Von Neumann entropy represented in phase space. (en)
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is Link from a Wikipage to another Wikipage of	Uncertainty principle Index of information theory articles Babenko–Beckner inequality Superfluid helium-4 Discrete Fourier transform Hirschman uncertainty Hirchman uncertainty
is Wikipage redirect of	Hirschman uncertainty Hirchman uncertainty
is foaf:primaryTopic of	wikipedia-en:Entropic_uncertainty

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