A Fundamental Property of Quantum-Mechanical Entropy

Dėnes Petz

Boaz Tamir, Ismael L. Paiva, Zohar Schwartzman-Nowik +1 more

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.

Alfred Wehrl

Jincheng Zhang

Quantum entanglement, a fundamental property of quantum mechanics, presents a unique challenge to traditional entropy calculations. This paper explores the development of a novel entropy calculation model based on quantum entanglement, aiming to improve the precision of measuring and predicting the evolution of entangled states. The core mechanism leverages the non-linear properties of entangled states to enable a more profound statistical analysis of quantum system evolution. The proposed model offers a significant advancement in quantifying the entanglement entropy, which has implications for quantum information security and quantum computation. This work addresses limitations of existing approaches by focusing on a fundamentally new framework for analyzing entanglement dynamics. The key contribution is the creation of an entanglement entropy measure that transcends classical approximations, offering a more accurate and robust representation of entanglement's statistical properties.

Ugo Farinelli, A. Gamba

Élliott H. Lieb, Mary Beth Ruskai

We have proved the strong subadditivity of quantum-mechanical entropy and the Wigner-Yanase-Dyson conjecture.Received 26 December 1972DOI:https://doi.org/10.1103/PhysRevLett.30.434©1973 American Physical Society