The time needed by a quantum system to reach a state fully distinguishable from the original one provides a natural way of determining how fast the corresponding dynamical evolution is. This orthogonality time admits a lower bound, expressible in terms of the energy's expectation value and the energy's standard deviation, that yields a 'quantum speed limit'. Composite quantum systems need entanglement in order to achieve this limit. So far, most studies on the connection between entanglement and the quantum speed limit have focused on the case of non-interacting systems. The connection between quantum speed and entanglement is systematically investigated here for the case of a system of two interacting qubits, taking into consideration all possible initial states that evolve into an orthogonal one. © 2013 IOP Publishing Ltd.

This work was partially supported by MEC grant FIS2011-23526 (Spain), by the Projects FQM-2445 and FQM-207 of the Junta de Andalucia, the grant FIS2011-24540 of the Ministerio de Innovacion y Ciencia (Spain), by the Conselleria d’Educacio, Cultura i Universitats (CAIB) and by FEDER (EU).

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