Entanglement resource theory of quantum channel

TL;DR

This paper develops a resource theory framework for quantifying entanglement in quantum channels, introducing new measures based on various entanglement concepts and proving their key properties.

Contribution

It presents two general methods for constructing entanglement measures of quantum channels and introduces specific measures based on Choi relative entropy, concurrence, and $k$-ME concurrence.

Findings

Proposed entanglement measures satisfy nonnegativity, monotonicity, and convexity.

Examples illustrate the application of these measures to quantum channels.

The measures enhance understanding of channel resources and their transformations.

Abstract

Quantum channels can represent dynamic resources, which are indispensable elements in many physical scenarios. To describe certain facets of nonclassicality of the channels, it is necessary to quantify their properties. In the framework of resource theory of quantum channel, we show two general ways of constructing entanglement measure of channels. We also present several entanglement measures of channels based on the Choi relative entropy of channels, concurrence and $k$-ME concurrence and give some specific examples. These entanglement measures of channels can deepen the cognizing about channel and advance the research on the transformation between coherent resources and entangled resources. In addition, we prove that these measures satisfy the properties including nonnegativity, monotonicity, convexity and so on.