Differential Geometry of Bipartite Quantum States

TL;DR

This paper explores the differential geometric structure of bipartite quantum states, detailing the manifold properties of pure states with various Schmidt ranks and coefficients, and calculating their dimensions.

Contribution

It provides explicit descriptions and dimension calculations of the manifolds of pure bipartite states with fixed Schmidt ranks or coefficients.

Findings

Explicit manifold structures for pure bipartite states

Dimension formulas for these manifolds

Detailed analysis of states with various Schmidt ranks

Abstract

We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given Schmidt ranks or Schmidt coefficients are explicitly presented. The dimensions of the related manifolds are calculated.