The entropy of quantum causal networks

TL;DR

This paper explores the entropy properties of quantum causal networks, introducing bounds and measures to quantify their information-theoretic aspects in quantum information theory.

Contribution

It presents a revised smooth max-relative entropy for quantum combs, bounds on hypothesis testing errors, and a new measure for quantum operator performance.

Findings

Established bounds on type II error in quantum hypothesis testing

Derived a lower bound for smooth max-relative entropy in asymptotic regimes

Proposed a new metric for quantifying quantum operator performance

Abstract

Quantum networks play a key role in many scenarios of quantum information theory. Here we consider the quantum causal networks in the manner of entropy. First we present a revised smooth max-relative entropy of quantum combs, then we present a lower and upper bound of a type II error of the hypothesis testing. Next we present a lower bound of the smooth max-relative entropy for the quantum combs with asymptotic equipartition. At last, we consider the score to quantify the performance of an operator. We present a quantity equaling to the smooth asymptotic version of the performance of a quantum positive operator.