| Issue |
4open
Volume 5, 2022
Logical Entropy
|
|
|---|---|---|
| Article Number | 2 | |
| Number of page(s) | 14 | |
| Section | Physics - Applied Physics | |
| DOI | https://doi.org/10.1051/fopen/2021005 | |
| Published online | 25 January 2022 | |
Research Article
Quantum logical entropy: fundamentals and general properties
1
Faculty of Interdisciplinary Studies, Bar-Ilan University, Ramat Gan 5290002, Israel
2
Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel
3
School of Computer Science and Engineering, The Hebrew University, Jerusalem 91904, Israel
* Corresponding author: eliahu.cohen@biu.ac.il
Received:
3
August
2021
Accepted:
1
November
2021
Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how this fundamental concept and other related definitions can be applied to the study of quantum systems with the use of quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.
Key words: Logical entropy / Quantum logical entropy / Distinctions / Post-selected systems
© B. Tamir et al., Published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.