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PACS number s : 03.65.Xp, 03.65.Ca, 03.67.Lx, 03.67.HkEntanglement 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 particlesThis work was partially supported by the Projects No.\udFQM-2445 and FQM-207 of the Junta de Andalucia  Spain ,\udthe MEC Grant No. FIS2005-02796  Spain  and FEDER\ud EU , by the Government of Balearic Islands  Spain , and by\udCONICET  Argentine Agency . A.B. acknowledges support\udfrom FPU Grant No. AP-2004-2962  MEC-Spain .Peer reviewe

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