# On the von Neumann rule in quantization

## TL;DR

This paper demonstrates that linear quantization maps into self-adjoint operators inherently violate the von Neumann rule when composed with real functions, highlighting a fundamental limitation in quantum operator mappings.

## Contribution

The paper reveals a fundamental incompatibility between linear quantization maps and the von Neumann rule, providing new insights into quantum operator theory.

## Key findings

- Linear quantization maps violate the von Neumann rule.
- The violation occurs upon post-composition with real functions.
- This highlights a fundamental limitation in quantum operator mappings.

## Abstract

We show that any linear quantization map into the space of self-adjoint operators in a Hilbert space violates the von Neumann rule on post-composition with real functions.