A-unital Operations and Quantum Conditional Entropy

TL;DR

This paper introduces A-unital channels as the largest class of channels that do not decrease quantum conditional entropy, providing tools to detect resourceful channels for quantum information tasks involving negative conditional entropy.

Contribution

It defines A-unital channels, characterizes their properties, and relates them to other classes, advancing the understanding of channels useful for negative quantum conditional entropy.

Findings

A-unital channels are the largest class of non-decreasing conditional entropy channels.

A-unital channels are the free operations for states with non-negative conditional entropy.

The paper provides a method to determine if a channel belongs to the A-unital class.

Abstract

Negative quantum conditional entropy states are key ingredients for information theoretic tasks such as superdense coding, state merging and one-way entanglement distillation. In this work, we ask: how does one detect if a channel is useful in preparing negative conditional entropy states? We answer this question by introducing the class of A-unital channels, which we show are the largest class of conditional entropy non-decreasing channels. We also prove that A-unital channels are precisely the completely free operations for the class of states with non-negative conditional entropy. Furthermore, we study the relationship between A-unital channels and other classes of channels pertinent to the resource theory of entanglement. We then prove similar results for ACVENN: a previously defined, relevant class of states and also relate the maximum and minimum conditional entropy of a state with its von Neumann entropy. The definition of A-unital channels naturally lends itself to a procedure for determining membership of channels in this class. Thus, our work is valuable for the detection of resourceful channels in the context of conditional entropy.