Superactivation of Quantum Channels is Limited by the Quantum Relative Entropy Function

TL;DR

This paper establishes that the superactivation of quantum channel capacities is fundamentally constrained by the properties of the quantum relative entropy function, revealing a deep mathematical link previously unknown.

Contribution

It uncovers a fundamental mathematical connection between quantum relative entropy and superactivation, applicable to all quantum channel capacities.

Findings

Superactivation is governed by quantum relative entropy properties.

Theoretical proof linking superactivation to quantum relative entropy.

Results applicable to all quantum channel capacities.

Abstract

In this work we prove that the possibility of superactivation of quantum channel capacities is determined by the mathematical properties of the quantum relative entropy function. Before our work this fundamental and purely mathematical connection between the quantum relative entropy function and the superactivation effect was completely unrevealed. We demonstrate the results for the quantum capacity; however the proposed theorems and connections hold for all other channel capacities of quantum channels for which the superactivation is possible.