Elementary open quantum states

TL;DR

This paper explores how symmetries in quantum states evolve from closed to open systems, defining elementary components via irreducible representations and illustrating with harmonic systems.

Contribution

It introduces a framework for understanding elementary open quantum states through symmetry and irreducible representations, extending previous closed system analysis.

Findings

Mixed states support a reduplicated symmetry in closed dynamics.

Symmetry reduces to a subgroup in open dynamics.

Elementary components are defined as operators in irreducible representations.

Abstract

It is shown that the mixed states of a closed dynamics support a reduplicated symmetry, which is reduced back to the subgroup of the original symmetry group when the dynamics is open. The elementary components of the open dynamics are defined as operators of the Liouville space in the irreducible representations of the symmetry of the open system. These are tensor operators in the case of rotational symmetry. The case of translation symmetry is discussed in more detail for harmonic systems.