Principal Component Analysis of Quantum Correlation

TL;DR

This paper applies principal component analysis to quantum correlation matrices in spin systems, revealing how PCA can identify meaningful axes related to qubit properties and polarization bases.

Contribution

It introduces the use of PCA on quantum correlation matrices for spin systems, linking principal components to polarization bases in Hilbert space.

Findings

PCA axes can align with polarization bases on the Bloch sphere.

Meaningful qubit properties emerge from PCA in 2x2 spin systems.

PCA provides insights into quantum correlations and observables.

Abstract

The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables are the Pauli matrices and a polarization vector is acting on the density matrix, meaningful results can be obtained by the PCA in terms of qubit properties. In particular, it is shown that by choosing, for example, the (x,z) spinors, the axes of the principal components (PC) coincide with the circular polarization basis on the Block Sphere.