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

DOI10.1007/s00041-018-9602-xzbMath1406.81051arXiv1712.09475OpenAlexW2963727407WikidataQ64960600 ScholiaQ64960600MaRDI QIDQ1710660

Nuno Costa Dias, João Nuno Prata, Maurice A. De Gosson

Publication date: 23 January 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.09475

zbMATH Keywords

Wigner distributionuncertainty principlesentropic relations

Mathematics Subject Classification ID

Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Measures of information, entropy (94A17) Analysis of variance and covariance (ANOVA) (62J10) Quantum state spaces, operational and probabilistic concepts (81P16)

Related Items

Hydrodynamic interpretation of generic squeezed coherent states: a kinetic theory, Coarse-graining and symplectic non-squeezing, Uncertainty principle for free metaplectic transformation, Uncertainty principle of complex-valued functions in specific free metaplectic transformation domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Remarks on the fact that the uncertainty principle does not determine the quantum state
• Born-Jordan quantization. Theory and applications
• Extensions of the Heisenberg-Weyl inequality
• Pseudo holomorphic curves in symplectic manifolds
• On a new Segal algebra
• When is the Wigner quasi-probability density non-negative?
• Inequalities in Fourier analysis
• Weyl transforms
• Proof of a conjecture on the supports of Wigner distributions
• On Wigner measures
• The uncertainty principle: A mathematical survey
• Foundations of time-frequency analysis
• On the reduction of the interferences in the Born-Jordan distribution
• On the twisted convolution product and the Weyl transformation of tempered distributions
• Admissible states in quantum phase space
• New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform
• The Narcowich-Wigner spectrum of a pure state
• Symplectic geometry and quantum mechanics
• The \(C^ *\)-algebras of a free Boson field
• \(C^ *\)-algèbres des systèmes canoniques. I
• Maximal covariance group of Wigner transforms and pseudo-differential operators
• Distributions of ℏ-positive type and applications
• A Note on Entropy
• Geometry and uncertainty
• Integral bounds for radar ambiguity functions and Wigner distributions
• Symplectic Methods in Harmonic Analysis and in Mathematical Physics
• Conditions for the convolution of two Wigner distributions to be itself a Wigner distribution
• Harmonic Analysis in Phase Space. (AM-122)
• Uncertainty principles for integral operators
• Variations on uncertainty principles for integral operators
• UNCERTAINTY PRINCIPLES FOR THE AMBIGUITY FUNCTION
• On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems
• On the principles of elementary quantum mechanics