Entanglement and the Lower Bounds on the Speed of Quantum Evolution

Abstract

The concept of quantum speed limit-time (QSL) was initially introduced as a lower bound to the time interval that a given initial state $ψ_I$ may need so as to evolve into a state orthogonal to itself. Recently [V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A {\bf 67}, 052109 (2003)] this bound has been generalized to the case where $ψ_I$ does not necessarily evolve into an orthogonal state, but into any other $ψ_F$. It was pointed out that, for certain classes of states, quantum entanglement enhances the evolution "speed" of composite quantum systems. In this work we provide an exhaustive and systematic QSL study for pure and mixed states belonging to the whole 15-dimensional space of two qubits, with $ψ_F$ a not necessarily orthogonal state to $ψ_I$. We display convincing evidence for a clear correlation between concurrence, on the one hand, and the speed of quantum evolution determined by the action of a rather general local Hamiltonian, on the other one.