Thursday 06 March 2025
The pursuit of eternal non-Markovianity in quantum systems has long been a topic of interest among physicists. Markovian processes, those that evolve independently and without memory, are well-studied and understood. However, eternal non-Markovianity (ENM) is a different beast altogether. It’s the phenomenon where a quantum system exhibits non-Markovian behavior indefinitely, defying our traditional understanding of how these systems work.
Recently, researchers have been exploring ENM in various contexts, including qubit maps – mathematical representations of quantum systems. Two types of qubit maps exist: unital and non-unital. Unital maps are those that preserve the overall probability density, while non-unital maps do not. In this case study, we’ll delve into the world of non-unital qubit maps and investigate whether ENM is possible in these systems.
The researchers began by examining a specific type of non-unital map called phase-covariant maps. These maps are characterized by their ability to preserve certain properties, such as phase coherence, while allowing for decoherence – the loss of quantum information due to interactions with an environment. The team found that even in this class of maps, ENM is not possible in the strong sense.
To put it simply, they showed that there cannot be a constant δ > 0 such that the decay rate becomes asymptotically negative. In other words, the non-unital part of these maps will never exhibit eternal non-Markovianity in the classical sense.
However, this doesn’t rule out quasi-ENM entirely. The researchers discovered that while ENM is forbidden in the strong sense, it’s possible for the decay rate to approach zero from below asymptotically. This is a weaker form of ENM, often referred to as weak ENM.
The implications of these findings are significant. They suggest that non-unital qubit maps may not be able to exhibit eternal non-Markovianity in their non-unital parts, but they can still display quasi-ENM behavior. This has important consequences for the study of quantum systems and our understanding of how they interact with their environments.
The researchers’ work also highlights the importance of understanding the differences between unital and non-unital qubit maps. While unital maps are well-studied, non-unital maps are still an area of active research.
Cite this article: “Eternal Non-Markovianity in Non-Unital Qubit Maps”, The Science Archive, 2025.
Quantum Systems, Markovianity, Non-Markovianity, Eternal Non-Markovianity, Qubit Maps, Unital Maps, Non-Unital Maps, Phase-Covariant Maps, Decoherence, Quasi
Reference: Vinayak Jagadish, R. Srikanth, “On the eternal non-Markovianity of qubit maps” (2025).
