Quantum Kinematics in Terms of Observable Quantities, and the Chirality of Entangled Two-Qubit States

We consider the kinematics of bi-partite quantum states as determined by observable quantities, in particular the Bloch vectors of the subsystems. In examining the simplest case of a pair of two-level systems, there is a remarkable connection between the presence of non-classical correlations and the chirality of the two bases generated by the singular value decomposition of the correlation matrix of the Bloch vectors. We investigate the limits imposed by quantum mechanics of this effect and it relationship with other methods on quantifying the system’s non-classical behaviour.