Quantum brachistochrone evolution of systems of two identical particles: The role of entanglement

Abstract

Entanglement plays a fundamental role in the brachistochrone evolution of composite quantum systems. In the case of composite systems with distinguishable subsystems quantum brachistochrone evolutions cannot be implemented without entanglement, excepting trivial cases in which only one of the subsystems evolves. Here we explore the connection between entanglement and time-optimal quantum evolution for systems of two identical particles, elucidating its dependence on the type of statistics obeyed by the particles