Quantum information in Riemannian spaces
| Autor: | Camara, Pablo G. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We develop a diffeomorphism-invariant formulation of differential entropy in Riemannian spaces, addressing the lack of an observer-independent notion of information for continuous variables in physical space. We extend this formulation to the quantum level by generalizing Wigner's quasiprobability density function to arbitrary Riemannian spaces and analytically continuing Shannon's differential entropy formula to incorporate contributions from intermediate virtual quantum states. We demonstrate this framework by computing the quantum phase space entropy of the harmonic oscillator in Minkowski and anti-de Sitter geometries. Additionally, we derive a generalized quantum entropic uncertainty relation, extending the Bialynicki-Birula and Mycielski inequality to curved spaces. Our work bridges concepts from information theory, geometry, and quantum physics to study quantum information in continuous and curved sample spaces. Comment: 13 pages, 4 figures, 1 appendix. v2: Improved presentation |
| Databáze: | arXiv |
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