Tight Upper Bound Of The Maximum Speed Of Evolution Of A Quantum State

I report a tight upper bound of the maximum speed of evolution from one quantum state $ρ$ to another $ρ'$ with fidelity $F(ρ,ρ')$ less than or equal to an arbitrary but fixed value under the action of a time-independent Hamiltonian. Since the bound is directly proportional to the average absolute deviation from the median of the energy of the state ${\mathscr D}E$, one may interpret ${\mathscr D}E$ as a meaningful measure of the maximum information processing capability of a system.

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