Probing the geometry of two-qubit state space by evolution

TL;DR

This paper provides a detailed geometric analysis of two-qubit state spaces under various Hamiltonian evolutions, including the effects of perturbations, and characterizes entanglement using the Fubini-Study metric and concurrence.

Contribution

It offers explicit geometric descriptions of two-qubit state manifolds under Hamiltonian evolution, including perturbations, and relates geometry to entanglement measures.

Findings

Explicit geometric descriptions of two-qubit state spaces.

Analysis of Hamiltonian perturbations on quantum geometry.

Characterization of entanglement via geometry and concurrence.

Abstract

We derive an explicit expressions for geometric description of state manifold obtained from evolution governed by a three parameter family of Hamiltonians covering most cases related to real interacting two-qubit systems. We discuss types of evolution in terms of the defining parameters and obtain relevant explicit description of the pure state spaces and their Remannian geometry with the Fubini-Study metric . In particular, there is given an analysis of the modification of known geometry of quantum state manifold by the linear noncommuting perturbation of the Hamiltonian. For families of states resulting from the unitary evolution, we characterize a degree of entanglement using the squared concurrence as its measure.