Quantum Fine-Grained Entropy

TL;DR

This paper introduces quantum fine-grained entropy as a new approach to better understand quantum entropy and entanglement, addressing longstanding issues like negative conditional entropy and the measure of quantumness.

Contribution

It proposes quantum fine-grained entropy, offering solutions to key problems in quantum information theory and thermodynamics that previous entropy measures could not resolve.

Findings

Resolves issues with negative quantum conditional entropy

Provides a new measure of entanglement and quantumness

Addresses the additivity conjecture of entanglement of formation

Abstract

Regarding the strange properties of quantum entropy and entanglement, e.g., the negative quantum conditional entropy, we revisited the foundations of quantum entropy, namely, von Neumann entropy, and raised the new method of quantum fine-grained entropy. With the applications in entanglement theory, quantum information processing, and quantum thermodynamics, we demonstrated the capability of quantum fine-grained entropy to resolve some notable confusions and problems, including the measure of entanglement and quantumness, the additivity conjecture of entanglement of formation etc, and the definition of temperature for single quantum system.