Geometry of Two-Qubit State and Intertwining Quaternionic Conformal Mapping Under Local Unitary Transformations

TL;DR

This paper explores the geometric structure of two-qubit quantum states under local unitary transformations, revealing how quaternionic conformal maps relate to quaternionic Möbius transformations, extending previous results in quantum information geometry.

Contribution

It demonstrates the intertwining role of quaternionic conformal maps between local unitary groups and quaternionic Möbius transformations, generalizing earlier findings.

Findings

Quaternionic conformal map links local unitary group and quaternionic Möbius transformation.

Extension of Lee et al.'s results to a broader quaternionic setting.

Geometric insights into two-qubit state transformations under local unitaries.

Abstract

In this paper the geometry of two-qubit systems under local unitary group $SO(2)\otimes SU(2)$ is discussed. It is shown that the quaternionic conformal map intertwines between this local unitary subgroup of $Sp(2)$ and the quaternionic M\"{o}bius transformation which is rather a generalization of the results of Lee et al (2002 Quantum Inf. Process. 1 129).