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

Abstract

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.