Entanglement and the quantum brachistochrone problemA. Borras1, C. Zander2, A. R. Plastino1, 2, 3, M. Casas1 and A. Plastino3
1 Departament de Física and IFISC-CSIC, Universitat de les Illes Balears - 07122 Palma de Mallorca, Spain
2 Physics Department, University of Pretoria - Pretoria 0002, South Africa
3 National University La Plata-CONICET - C.C. 727, 1900 La Plata, Argentina
received 10 September 2007; accepted in final form 27 November 2007; published February 2008
published online 31 December 2007
Entanglement is closely related to some fundamental features of the dynamics of composite quantum systems: quantum entanglement enhances the "speed" of evolution of certain quantum states, as measured by the time required to reach an orthogonal state. The concept of "speed" of quantum evolution constitutes an important ingredient in any attempt to determine the fundamental limits that basic physical laws impose on how fast a physical system can process or transmit information. Here we explore the relationship between entanglement and the speed of quantum evolution in the context of the quantum brachistochrone problem. Given an initial and a final state of a composite system we consider the amount of entanglement associated with the brachistochrone evolution between those states, showing that entanglement is an essential resource to achieve the alluded time-optimal quantum evolution.
03.65.Xp - Tunneling, traversal time, quantum Zeno dynamics.
03.65.Ca - Formalism.
03.67.Lx - Quantum computation.
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