Version 1
: Received: 15 June 2023 / Approved: 15 June 2023 / Online: 15 June 2023 (09:47:41 CEST)
How to cite:
Zelenov, E. Coherent States of the p-Adic Heisenberg Group and Entropic Uncertainty Relations. Preprints2023, 2023061116. https://doi.org/10.20944/preprints202306.1116.v1
Zelenov, E. Coherent States of the p-Adic Heisenberg Group and Entropic Uncertainty Relations. Preprints 2023, 2023061116. https://doi.org/10.20944/preprints202306.1116.v1
Zelenov, E. Coherent States of the p-Adic Heisenberg Group and Entropic Uncertainty Relations. Preprints2023, 2023061116. https://doi.org/10.20944/preprints202306.1116.v1
APA Style
Zelenov, E. (2023). Coherent States of the <em>p</em>-Adic Heisenberg Group and Entropic Uncertainty Relations. Preprints. https://doi.org/10.20944/preprints202306.1116.v1
Chicago/Turabian Style
Zelenov, E. 2023 "Coherent States of the <em>p</em>-Adic Heisenberg Group and Entropic Uncertainty Relations" Preprints. https://doi.org/10.20944/preprints202306.1116.v1
Abstract
Properties of coherent states for the Heisenberg group over a field of $p$-adic numbers are investigated. It turns out that coherent states form an orthonormal basis. The family of all such bases is parametrized by a set of self-dual lattices in the phase space. The Wehrl entropy $S_W$ is considered and its properties are investigated. In particular, it is proved that $S_W\geq 0$ and vanishes only on coherent states. For a pair of different bases of coherent states, an entropic uncertainty relation is obtained. It is shown that the lower bound for the sum of the corresponding Wehrl entropies is given by the distance between the lattices. The proof uses the fact that the bases of coherent states corresponding to a pair of lattices are mutually unbiased.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
