The speed limit, that is, the minimal time to transition between two easily distinguishable states, such as the north and south poles representing up and down states of a quantum spin (top), is characterized by a well-known relationship. But the speed limit between two states not entirely distinguishable, which correspond to states of arbitrary latitude and longitude whether on or within the sphere of all possible states of a quantum spin (bottom), was unknown until two UC Berkeley physical chemists calculated it. Ty Volkoff image.

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