Related papers: Towards entropic uncertainty relations for non-regular Hilbert spaces

Towards entropic uncertainty relations for non-regular Hilbert spaces

URL: http://arxiv.org/abs/2503.19216v1
Date: Mon, 24 Mar 2025 23:41:50 GMT
Title: Towards entropic uncertainty relations for non-regular Hilbert spaces
Authors: Alejandro Corichi, Angel Garcia Chung, Federico Zadra,
Abstract summary: The Entropic Uncertainty Relations (EUR) result from inequalities that are intrinsic to the Hilbert space and its dual with no direct connection to the Canonical Commutation Relations.<n>The analysis of these EUR in the context of singular Hilbert spaces has not been addressed.
Score: 44.99833362998488
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: The Entropic Uncertainty Relations (EUR) result from inequalities that are intrinsic to the Hilbert space and its dual with no direct connection to the Canonical Commutation Relations. Bialynicky-Mielcisnky obtained them in \cite{bialynicki1975uncertainty} attending Hilbert spaces with a Lebesgue measure. The analysis of these EUR in the context of singular Hilbert spaces has not been addressed. Singular Hilbert spaces are widely used in scenarios where some discretization of the space (or spacetime) is considered, e.g., loop quantum gravity, loop quantum cosmology and polymer quantum mechanics. In this work, we present an overview of the essential literature background and the road map we plan to follow to obtain the EUR in polymer quantum mechanics.

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