# Resource theory of entanglement for bipartite quantum channels

## TL;DR

This paper extends resource theories in quantum information from states to channels, establishing fundamental bounds and measures for entanglement in bipartite quantum channels, advancing understanding of quantum channel transformations.

## Contribution

It introduces a resource theory framework for bipartite quantum channels, defining entanglement measures and bounds for information processing tasks, and interprets the max-Rains information as a divergence.

## Key findings

- Established bounds on channel entanglement tasks
- Defined entanglement measures like logarithmic negativity and κ-entanglement
- Provided a divergence interpretation for max-Rains information

## Abstract

The traditional perspective in quantum resource theories concerns how to use free operations to convert one resourceful quantum state to another one. For example, a fundamental and well known question in entanglement theory is to determine the distillable entanglement of a bipartite state, which is equal to the maximum rate at which fresh Bell states can be distilled from many copies of a given bipartite state by employing local operations and classical communication for free. It is the aim of this paper to take this kind of question to the next level, with the main question being: What is the best way of using free channels to convert one resourceful quantum channel to another? Here we focus on the the resource theory of entanglement for bipartite channels and establish several fundamental tasks and results regarding it. In particular, we establish bounds on several pertinent information processing tasks in channel entanglement theory, and we define several entanglement measures for bipartite channels, including the logarithmic negativity and the $\kappa$-entanglement. We also show that the max-Rains information of [B\"auml et al., Physical Review Letters, 121, 250504 (2018)] has a divergence interpretation, which is helpful for simplifying the results of this earlier work.