A Parametrization of Bipartite Systems Based on SU(4) Euler Angles

TL;DR

This paper introduces a comprehensive SU(4) Euler angle parametrization for all two-qubit density matrices, facilitating calculations of entanglement and separability in quantum information processing.

Contribution

It provides a generalized Euler angle parametrization for SU(4) and two-qubit states, including Haar measure and volume element derivation, enhancing quantum state analysis tools.

Findings

Derived the Haar measure for SU(4) using the parametrization

Applied the parametrization to analyze Peres-Horodecki separability criteria

Facilitated calculations of entangled two-qubit states

Abstract

In this paper we give an explicit parametrization for all two qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing. To accomplish this we present a generalized Euler angle parametrization for SU(4) and all possible two qubit density matrices. The important group-theoretical properties of such a description are then manifest. We thus obtain the correct Haar (Hurwitz) measure and volume element for SU(4) which follows from this parametrization. In addition, we study the role of this parametrization in the Peres-Horodecki criteria for separability and its corresponding usefulness in calculating entangled two qubit states as represented through the parametrization.