Quantumness of channels

TL;DR

This paper introduces an intuitive and computationally simple measure of the quantumness of quantum channels based on non-commutativity, and validates it against known noise channels, aligning well with existing coherence-based measures.

Contribution

It proposes a new measure of quantumness of channels rooted in non-commutativity, applicable to various noise models, and compares favorably with existing coherence-based metrics.

Findings

The measure aligns with $l_1$-norm coherence measures.

It effectively characterizes both Markovian and non-Markovian noise channels.

The measure is easy to compute and intuitive.

Abstract

The reliability of quantum channels for transmitting information is of profound importance from the perspective of quantum information. This naturally leads to the question as how well a quantum state is preserved when subjected to a quantum channel. We propose a measure of quantumness of channels based on non-commutativity of quantum states that is intuitive and easy to compute. We apply the proposed measure to some well known noise channels, both Markovian as well as non-Markovian and find that the results are in good agreement with those from a recently introduced $l_1$-norm coherence based measure.