Issue
EPL
Volume 81, Number 3, February 2008
Article Number 30007
Number of page(s) 5
Section General
DOI http://dx.doi.org/10.1209/0295-5075/81/30007
Published online 31 December 2007
EPL, 81 (2008) 30007
DOI: 10.1209/0295-5075/81/30007

Entanglement and the quantum brachistochrone problem

A. 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

arplastino@maple.up.ac.za

received 10 September 2007; accepted in final form 27 November 2007; published February 2008
published online 31 December 2007

Abstract
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.

PACS
03.65.Xp - Tunneling, traversal time, quantum Zeno dynamics.
03.65.Ca - Formalism.
03.67.Lx - Quantum computation.

© EPLA 2008