Entanglement Entropy in Quantum Mechanics: An Algebraic Approach

An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^{\ast }$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of this approach to the study of entanglement measures for systems of identical particles are outlined. The ambiguities in the definition of entropy within this approach are then related to the action of unitaries in the commutant of the representation and their relation to modular theory explained.