  Quantum mechanics imposes fundamental constraints known as quantum speed
limits (QSLs) on the information processing speed of all quantum systems. Every
QSL known to date comes from the restriction imposed on the evolution time
between two quantum states through the value of a single system observable such
as the mean energy relative to its ground state. So far these restrictions only
place upper bounds on the information processing speed of a quantum system.
Here I report QSLs each with permissible information processing speeds
separated by forbidden speed intervals. They are found by a systematic and
efficient procedure that takes the values of several compatible system
observables into account simultaneously. This procedure generalizes almost all
existing QSL proofs; and the new QSLs show a novel first order phase transition
in the minimum evolution time.
