Uncertainty of Quantum States

Abstract: The uncertainty of a quantum state is given by the composition of two components. The first is called the quantum component and is given by the probability distribution of an observable relative to the state. The second is the classical component which is an uncertainty function that is applied to the first component. We characterize uncertainty functions in terms of four axioms. We then study four examples called variance, entropy, geometric and sine uncertainty functions. The final section presents the general theory of state uncertainty.