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

TL;DR

This paper explores how observable quantities like Bloch vectors determine the kinematics of bipartite quantum states, revealing a link between non-classical correlations and the chirality of generated bases, with implications for understanding quantum non-classicality.

Contribution

It introduces a novel connection between non-classical correlations and basis chirality in two-qubit systems using observable quantities, expanding the understanding of quantum state kinematics.

Findings

Non-classical correlations relate to basis chirality.

Quantum limits constrain this relationship.

The approach offers new insights into quantum non-classicality.

Abstract

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.