Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)-symmetric systems

The article delves into the fundamental postulates of quantum theory, specifically focusing on the Hermiticity of the Hamiltonian and its implications for the dynamics of open quantum systems. It discusses the approximate approach of handling the Schrödinger equation to describe the dynamics of open quantum systems, which often involves non-Hermitian Hamiltonians. The article explores the exceptional points (EPs) in non-Hermitian systems, which can exhibit real spectra under certain symmetries, and their applications in various fields such as optics, electronics, and acoustics. It also addresses the issue of decoherence control in quantum information processing and the definition of Markovianity in quantum processes. The article introduces the Hilbert–Schmidt speed (HSS) as a measure to detect exceptional points and characterize phase transitions in (anti-)symmetric systems, highlighting its efficiency and practical advantages over other methods. The relationship between HSS and quantum Fisher information (QFI) is also discussed, showing their similar qualitative dynamics and potential applications in quantum estimation. The article concludes by emphasizing the need for further research on the applicability of witnesses of non-Markovianity in both Hermitian and non-Hermitian systems.