On coherence of quantum operations by using Choi-Jamio{\l}kowski isomorphism

TL;DR

This paper investigates the coherence of quantum operations using the Choi-Jamiołkowski isomorphism within resource theory, defining new superoperations and coherence measures, and analyzing their properties and specific cases like single-qubit unitaries.

Contribution

It introduces a framework for analyzing quantum operation coherence via Choi-Jamiołkowski isomorphism, defining new superoperations and coherence measures, and studying their properties.

Findings

Sets of superoperations are closed under compound operations and convex combinations.

Fidelity coherence measure for quantum operations is introduced and exactly computed for single-qubit unitaries.

The framework links quantum operation coherence to resource theory concepts, enabling new analysis methods.

Abstract

In quantum information, most information processing processes involve quantum channels. One manifestation of a quantum channel is quantum operation acting on quantum states. The coherence of quantum operations can be considered as a quantum resource, which can be exploited to perform certain quantum tasks. From the viewpoint of Choi-Jamio{\l}kowski isomorphism, we study the coherence of quantum operations in the framework of resource theory. We define the phase-out superoperation and give the operation which transforms the Choi-Jamio{\l}kowski state of a quantum operation to the Choi-Jamio{\l}kowski state of the another quantum operation obtained by using the phase-out superoperation to act on the quantum operation. The set of maximally incoherent superoperations, the set of nonactivating coherent superoperations and the set of de-phase incoherent superoperations are defined and we prove that these sets are closed to compound operation and convex combination of quantum superoperations. Further, we introduce the fidelity coherence measure of quantum operations and obtain the exact form of the fidelity coherence measure of the unitary operations on the single qubit.