Quantum-correlation breaking channels, quantum conditional probability and Perron-Frobenius theory

TL;DR

This paper explores quantum channels that break correlations using quantum conditional probability and Perron-Frobenius theory, extending previous results to more general channels.

Contribution

It introduces a quantum analog of Perron-Frobenius theorem to generalize correlation-breaking results to arbitrary quantum channels.

Findings

Generalized correlation-breaking conditions for quantum channels.

Extended broadcasting results to broader classes of channels.

Connected quantum and classical channel behaviors through new theoretical tools.

Abstract

Using the quantum analog of conditional probability and classical Bayes theorem we discuss some aspects of quantum-classical and classical-classical channels in connection to the recent paper J. Korbicz, P. Horodecki, and R. Horodecki, "Quantum-correlation breaking channels, broadcasting scenarios, and finite Markov chains". Applying the quantum analog of Perron-Frobenius theorem we generalize the result of Korbicz et. al. on full and spectrum broadcasting from quantum-classical channels to arbitrary channels.