Generalized Euler Angle Paramterization for SU(N)

TL;DR

This paper introduces a generalized Euler angle parameterization for SU(N), providing a systematic way to describe these groups and their Haar measure, with applications to quantum systems like qubits and qutrits.

Contribution

It extends previous SU(4) parameterization to SU(N), deriving formulas for Haar measure and demonstrating applications to quantum state representations.

Findings

Derived a generalized Euler angle parameterization for SU(N)

Provided formulas for Haar measure and volume calculations

Applied the parameterization to quantum systems like qubits and qutrits

Abstract

In a previous paper (math-ph/0202002) an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov's volume formula for SU(N) will also be derived. As an example of this parameterization's usefulness, the density matrix parameterization and invariant volume element for a qubit/qutrit, three qubit and two three-state systems, also known as two qutrit systems, will also be given.