Unique determination and generation of rank-two single-qubit quantum channels

Abstract

An important problem in quantum technologies is to generate a target quantum evolution of an open quantum system. As a core element, it requires the ability to determine whether the actual evolution of the system coincides with the target evolution. For generation of unitary quantum channels in open quantum systems, it was shown by Goerz et al (2014 New J. Phys. 16 055012) that for determining whether the actual evolution coincides with a target unitary it is sufficient to compare their action on three special density matrices. In this work, we consider controlled generation and unique determination of non-unitary quantum channels in open quantum systems with particular emphasis on rank-two single-qubit quantum channels. We prove that for a unique determination of such quantum channels it is sufficient to consider their action on only three special density matrices. Based on this theoretical result, we numerically investigate generation of various target non-unitary single-qubit quantum channels in open quantum systems using coherent and incoherent controls.