Decomposition of symmetric separable states and ground state energy of bosonic systems

TL;DR

This paper explores the convex decomposition of symmetric separable states into pure product states, emphasizing geometric aspects and applications to the ground state energies of infinite bosonic systems.

Contribution

It provides a geometric perspective on decomposing symmetric separable states and applies this to analyze ground state energies in bosonic systems.

Findings

Symmetric separable states can be decomposed into symmetric pure product states.

The decomposition relates to convex geometry and numerical ranges.

Applications to ground state energy problems in bosonic systems.

Abstract

We prove that every symmetric separable state admits a convex decomposition into symmetric pure product states. While the result is not new in itself, here we focus on convex geometry. We discuss the decomposition in the context of numerical ranges and ground state problems of infinite bosonic systems.