Uncertainty of Quantum States

TL;DR

This paper develops a comprehensive framework for understanding quantum state uncertainty by decomposing it into quantum and classical components, characterizing uncertainty functions, and analyzing specific examples.

Contribution

It introduces axioms to characterize uncertainty functions and explores four specific types, advancing the theoretical understanding of quantum state uncertainty.

Findings

Uncertainty functions can be characterized by four axioms.

Variance, entropy, geometric, and sine are key examples of uncertainty functions.

A general theory of state uncertainty is developed.

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.