Geometry and topology of CC and CQ states

TL;DR

This paper explores the geometric and topological properties of bipartite classical-quantum (CQ) and classical-classical (CC) states, revealing their distinct characteristics in the state space.

Contribution

It introduces a novel geometric and topological framework to distinguish CC and CQ states based on Euler-Poincaré characteristics and symplectic structures.

Findings

CC and CQ states have non-zero Euler-Poincaré characteristics

They possess a symplectic structure in the geometric analysis

These properties distinguish them topologically and geometrically

Abstract

We show that multipartite mixed bipartite CC and CQ states are geometrically and topologically distinguished in the space of states. They are characterized by non-vanishing Euler-Poincar\'{e} characteristics on the topological side and by the existence of symplectic structure on the geometric side.