Tight upper bound of the maximum speed of evolution of a quantum state
H. F. Chau · Physical Review A · 2010
I report a tight upper bound of the maximum speed of evolution from one quantum state $\ensuremath{\rho}$ to another ${\ensuremath{\rho}}^{\ensuremath{'}}$ with fidelity $F(\ensuremath{\rho},{\ensuremath{\rho}}^{\ensuremath{'}})$ 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 $\mathcal{D}E$, one may interpret $\mathcal{D}E$ as a meaningful measure of the maximum information-processing capability of a system.