Generalized Kraus Operators for the One-Qubit Depolarizing Quantum Channel

Abstract

© 2017, Sociedade Brasileira de Física. 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 developed method (Andersson et al. J. Mod. Opt. 54, 1695 2007), we derive the Kraus operators starting from the microscopic Hamiltonian model, i.e., from the proper master equation, of the one-qubit depolarizing channel. Those Kraus operators generalize the standard counterparts, which are widely used in the literature. Comparison of the standard and the here obtained Kraus operators is performed via investigating dynamical change of the Bloch sphere volume, entropy production, and the open system’s state trace distance. We compare the generalized with the standard Kraus operators for both single qubit and regarding the occurrence of the entanglement sudden death for a pair of initially correlated qubits. We find that the generalized Kraus operators describe the less deteriorating quantum channel than the standard ones.