Optimal decomposition of incoherent qubit channel

TL;DR

This paper demonstrates that any incoherent qubit channel can be optimally decomposed into four incoherent Kraus operators, revealing differences between Kraus rank and incoherent rank and discussing applications.

Contribution

It provides a proof that any incoherent qubit channel admits a decomposition into four incoherent Kraus operators, establishing an optimal decomposition method.

Findings

Any incoherent qubit channel can be decomposed into four incoherent Kraus operators.

Kraus rank and incoherent rank differ even for qubit channels.

The paper discusses applications of the optimal decomposition.

Abstract

We show that any incoherent qubit channel could be decomposed into four incoherent Kraus operators. The proof consists in showing existence of four incoherent Kraus operators by decomposing the corresponding Choi-Jamio\l{}kowski-Sudarshan matrix. We mention some applications of this optimal decomposition. We also show that the Kraus rank and incoherent rank are different even for qubit channel.