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Quantum Speed Limit With Forbidden Speed Intervals

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.