# Against the Tyranny of Pure States in Quantum Theory

## TL;DR

This paper critiques the inconsistent definitions of pure states in quantum mechanics, revealing fundamental issues with current conceptual frameworks and emphasizing the need for clearer operational interpretations.

## Contribution

It identifies and formalizes the inconsistencies between two definitions of purity in quantum theory, providing a theorem that exposes their fundamental incompatibility.

## Key findings

- Operational and trace-invariant purity definitions are incompatible.
- Theorem demonstrating the fundamental inconsistency between the two purity notions.
- Highlights conceptual issues in the standard interpretation of pure states.

## Abstract

We argue that the notion of pure sate within Standard Quantum Mechanics is presently applied within the specialized literature in relation to two mutually inconsistent definitions. While the first (operational purity) provides a basis-dependent definition which makes reference to the certain prediction of measurement outcomes, the latter (trace-invariant purity) provides a purely abstract invariant definition which lacks operational content. In this work we derive a theorem which exposes the serious inconsistencies existent within these two incompatible definitions of purity.