Differential Geometry on SU(3) with Applications to Three State Systems

Abstract

The left and right invariant vector fields are calculated in an ``Euler angle'' type parameterization for the group manifold of SU(3), referred to here as Euler coordinates. The corresponding left and right invariant one-forms are then calculated. This enables the calculation of the invariant volume element or Haar measure. These are then used to describe the density matrix of a pure state and geometric phases for three state systems.

17 pages, LaTeX2e, Accepted by J. Math. Phys

References in corpus (2)

• Resource Letter GPP-1: Geometric Phases in Physics
• SU(3) Revisited

Cited by in corpus (40)

• Generalized Euler Angle Paramterization for SU(N)
• Hilbert--Schmidt volume of the set of mixed quantum states
• Qutrit Entanglement
• A Parametrization of Bipartite Systems Based on SU(4) Euler Angles
• Generalized Euler Angle Parameterization for U(N) with Applications to SU(N) Coset Volume Measures
• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• A priori Probabilities of Separable Quantum States
• A general approach to quantum mechanics as a statistical theory
• Volumes of Compact Manifolds
• Berry and Pancharatnam Topological Phases of Atomic and Optical Systems
• Bures Measures over the Spaces of Two and Three-Dimensional Density Matrices
• SU(3) Revisited
• Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
• Geometry of mixed states and degeneracy structure of geometric phases for multi-level quantum systems. A unitary group approach
• How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics
• Quarks with Twisted Boundary Conditions in the Epsilon Regime
• Volumes of conditioned bipartite state spaces
• Berry's phase for compact Lie groups
• Localization in Quantum Walks on a Honeycomb Network
• Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases
• Topological Phases near a Triple Degeneracy
• Affine Maps of the Polarization Vector for Quantum Systems of Arbitrary Dimension
• Parameter differentiation and quantum state decomposition for time varying Schroedinger equations
• Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
• On the Hamiltonian reduction of geodesic motion on SU(3) to SU(3)/SU(2)
• On the family of Wigner functions for N-level quantum system
• Ramanujan complexes and Golden Gates in PU(3)
• Measure of the density of quantum states in information geometry and its application in the quantum multi-parameter estimation
• Entanglement gauge and the non-Abelian geometric phase with two photonic qubits
• On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices
• An Explicit Computation of the Bures Metric Over the Space of $N$-Dimensional Density Matrices
• Twisted CP(N-1) instanton projectors and the N-level quantum density matrix
• Non Abelian structures and the geometric phase of entangled qudits
• Generation of tripartite entangled states with fermionic systems
• Quantum covariant derivative
• Chiral symmetry: An analytic $SU(3)$ unitary matrix
• Time Evolution Operators for Periodic SU(3)
• Entangling power of symmetric multiqubit systems: a geometrical approach
• Higher order Magnus expansions for driven two-level quantum dynamics
• Physically motivated decompositions of single-qutrit gates