On coherence of quantum operations by using Choi–Jamiołkowski isomorphism

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–Jamiołkowski isomorphism, we study the coherence of quantum operations in the framework of resource theory. We study the phase-out superoperation and give the operation which transforms the Choi–Jamiołkowski state of a quantum operation to the Choi–Jamiołkowski 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 investigated 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.