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 $\rho$ to another $\rho'$ with fidelity $F(\rho,\rho')$ 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.Comment: 4 pages, 1 figure, minor changes with an additional reference added, to appear in PR

The ideal energy of classical lattice dynamics

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335