Discuss the concept of entanglement entropy and its relevance in characterizing the degree of entanglement in a quantum system.

Entanglement entropy is a measure of the degree of entanglement between subsystems of a quantum system. It quantifies the amount of information needed to describe the entangled state of one subsystem when the state of the other subsystem is known. High entanglement entropy indicates a high degree of entanglement, which is relevant in many areas such as quantum computing, quantum phase transitions, and understanding the thermal properties of quantum systems.