Generalized Kraus operators for the one-qubit depolarizing quantum channel

TL;DR

This paper derives generalized Kraus operators for the one-qubit depolarizing channel from a microscopic Hamiltonian model, revealing differences from standard operators in their impact on quantum states.

Contribution

It introduces a method to derive generalized Kraus operators directly from microscopic Hamiltonian models, extending the standard form used in quantum information.

Findings

Generalized Kraus operators differ from standard ones in their effect on the Bloch sphere.

The standard depolarizing channel causes more deterioration than the generalized version.

Comparison metrics include entropy production and trace distance changes.

Abstract

Microscopic Hamiltonian models of the composite system "open system + environment" typically do not provide the operator-sum Kraus form of the open system's dynamical map. With the use of a recently de- veloped method [16], we derive the Kraus operators starting from the mi- croscopic Hamiltonian model, i.e. from the proper master equation, of the one-qubit depolarizing channel. Those Kraus operators generalize the stan- dard counterparts, which are widely used in the literature. Comparison of the standard and the here obtained Kraus operators is performed via inves- tigating dynamical change of the Bloch sphere volume, entropy production and the open system's state trace distance. We find that the standard depo- larizing channel is more deteriorating than the generalized one.