# Mixed Quantum States with Variable Planck Constant

## TL;DR

This paper investigates how potential variations in Planck's constant could influence quantum states, revealing that such changes can significantly alter their purity and classicality, with implications for quantum-classical transitions.

## Contribution

It explores the effects of variable Planck's constant on quantum states, highlighting the sensitivity of state purity and the possibility of quantum-classical state transitions.

## Key findings

- Quantum state purity is highly sensitive to changes in Planck's constant.
- Quantum states can evolve into classical states and vice versa due to h variations.
- Mathematical difficulties prevent complete classification of these state transitions.

## Abstract

Recent cosmological measurements tend to confirm that the fine structure constant {\alpha} is not immutable and has undergone a tiny variation since the Big Bang. Choosing adequate units, this could also reflect a variation of Planck's constant h. The aim of this Letter is to explore some consequences of such a possible change of h for the pure and mixed states of quantum mechanics. Surprisingly enough it is found that not only is the purity of a state extremely sensitive to such changes, but that quantum states can evolve into classical states, and vice versa. A complete classification of such transitions is however not possible for the moment being because of yet unsolved mathematical difficulties related to the study of positivity properties of trace class operators.