Generalizing Stratonovich-Weyl axioms for composite systems

TL;DR

This paper extends the Stratonovich-Weyl axioms to better accommodate the phase space representation of composite quantum systems, emphasizing the importance of prior knowledge about system composition.

Contribution

It proposes a generalized set of Stratonovich-Weyl axioms tailored for composite quantum systems, enhancing the phase space approach in quantum mechanics.

Findings

Extended axioms accommodate composite system structures

Improved phase space mappings for complex quantum systems

Highlights the role of prior knowledge in quantum state representations

Abstract

The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich-Weyl axioms. Arguments are given in favour of a certain extension of the axioms, provided that there is a priori knowledge about the composite nature of the quantum system.