Cohering and de-cohering power of quantum channels

TL;DR

This paper introduces and analyzes the concepts of cohering and de-cohering power of quantum channels, providing simplified calculation methods and exploring their properties and implications for quantum information processing.

Contribution

It defines cohering and de-cohering power using axiomatic coherence measures, simplifies their computation, and investigates their properties in various quantum channels and unitary operations.

Findings

Quantum channels can have cohering power, contrary to initial assumptions.

A qubit unitary map has equal cohering and de-cohering power in any basis.

Derived relations between powers of unitary qubit gates and their tensor products.

Abstract

We introduce the concepts of cohering and de-cohering power of quantum channels. Using the axiomatic definition of coherence measure, we show that the optimizations required for calculations of these measures can be restricted to pure input states and hence greatly simplified. We then use two examples of this measure, one based on the skew information and the other based on $l-1$ norm, we find the cohering and de-cohering measures of a number of one, two and n-qubit channels. Contrary to a view at first sight, it is seen that quantum channels can have cohering power. It is also shown that a specific property of a qubit unitary map, is that it has equal cohering and de-cohering power in any basis. Finally we derive simple relations between cohering and de-cohering powers of unitary qubit gates and their tensor products, results which have physically interesting implications.