Towards entropic uncertainty relations for non-regular Hilbert spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915520511475712 |
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| author | Corichi, Alejandro Chung, Angel Garcia Zadra, Federico |
| author_facet | Corichi, Alejandro Chung, Angel Garcia Zadra, Federico |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_19216 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards entropic uncertainty relations for non-regular Hilbert spaces Corichi, Alejandro Chung, Angel Garcia Zadra, Federico General Relativity and Quantum Cosmology Mathematical Physics Quantum Physics 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. |
| title | Towards entropic uncertainty relations for non-regular Hilbert spaces |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2503.19216 |