Quantum Fine-Grained Entropy

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.