AUTHOR=Shrikant U. , Mandayam Prabha TITLE=Quantum non-Markovianity: Overview and recent developments JOURNAL=Frontiers in Quantum Science and Technology VOLUME=2 YEAR=2023 URL=https://www.frontiersin.org/journals/quantum-science-and-technology/articles/10.3389/frqst.2023.1134583 DOI=10.3389/frqst.2023.1134583 ISSN=2813-2181 ABSTRACT=

In the current era of noisy intermediate-scale quantum (NISQ) devices, research on the theory of open system dynamics has a crucial role to play. In particular, understanding and quantifying memory effects in quantum systems is critical to gain a better handle on the effects of noise in quantum devices. The main focus of this review is to address the fundamental question of defining and characterizing such memory effects—broadly referred to as quantum non-Markovianity—utilizing various approaches. We first discuss the two-time-parameter maps approach to open system dynamics and review the various notions of quantum non-Markovianity that arise in this paradigm. We then discuss an alternate approach to quantum stochastic processes based on the quantum combs framework, which accounts for multi-time correlations. We discuss the interconnections and differences between these two paradigms and conclude with a discussion on the necessary and sufficient conditions for quantum non-Markovianity.