Research Projects

Recent studies have explored the convex combination of quantum channels, particularly non-Markovianity, which can be produced by mixing qubit or higher-dimensional quantum dynamical semigroups or more general (non-)Markovian channels. This has led to the investigation of the measure of invertible (semigroup) channels obtained by mixing qudit Pauli channels. However, these studies have mainly focused on unital channels. This project aims to formulate and characterize the nonunital equivalents of the generalized amplitude damping channel in the context of qubits and higher-dimensional systems using mutually unbiased bases in prime power dimensions. The goal is to specify the parameter ranges under which semigroup, (non-)Markovian, or (non-)invertible behavior is obtained. The next step is to consider the convex combinations of the semigroups and more general invertible channels of this nonunital type, studying the necessary and sufficient conditions under which they lead to the production of (non-)Markovianity and (non-)invertibility. This will pave the way for studying the geometry of the non-Markovian and/or non-invertible regions in the parameter space of these nonunital channels, particularly to understand their dimensional scaling. The geometric property studied will be useful to formulate a potential convex resource theory for noninvertibility of generalized nonunital channels, where noninvertible channels can act as a limitative factor when applied to quantum information tasks. This research will deepen our understanding of open system dynamics from a quantum information theoretic perspective, providing new insight into the structure of nonunital quantum channels for qubits or qudits.