Principal Component Analysis of quantum correlation

The concept of the quantum correlation matrix for observables leads to the application of PCA (Principal Component Analysis) also for quantum systems in Hilbert space. The consistency of PCA for quantum systems, is illustrated in the case of a qubit system with two Pauli matrices as observables and a density matrix polarized along the third one. As the main application of this theory, it is shown that the principal components are able to generate a class of quantum channels and depolarizing operators mapping density matrices (even pure states) to maximally mixed states.