The year 2026 marks the fiftieth anniversary of the two seminal papers in which Gorini, Kossakowski, and Sudarshan, and independently Lindblad, characterized the generators of completely positive quantum dynamical semigroups. We revisit the conceptual and historical route leading to the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation and examine several of its early developments and consequences. Our aim is to show how several initially separate mathematical and physical ideas converged in the GKLS structure theorem, imme- diately opening the way to manifold consequences for the description of dissipative quantum phenomena and how that theorem, fifty years later, remains both a foundational result and an active framework for open quantum dynamics.
We investigate the decoherence dynamics of a hydrogen atom interacting with a thermal environment through momentum–momentum coupling within the quantum Brownian motion (QBM) framework. Unlike the conventional position coupling paradigm, we consider a bilinear interaction Hamiltonian in which the radial momentum of the hydrogen atom couples to the momenta of environmental oscillators. Using the Born–Markov approximation, we derive a master equation for the reduced density operator of the hydrogen atom. The radial dynamics are treated algebraically using ladder operators, allowing us to obtain a closed-form expression for the time evolution of the momentum operator in the interaction picture. We compute the environment induced decoherence coefficient in terms of the environmental spectral density and a characteristic hydrogenic frequency. For a Lorentz–Drude spectral density, we analyze how decoherence rate varies with the hydrogen atom principal and angular momentum quantum numbers. Our results show that decoherence is strongest for low-[Formula: see text], low-[Formula: see text] states, while it is significantly reduced for Rydberg and high angular momentum states due to their narrow radial momentum distributions. This reduction reflects a relative robustness of highly excited hydrogenic states against environmental noise, which is relevant for applications relying on long atomic coherence times.
In classical information theory, the most important theorems are the cod-ing theorems, which were discussed by calculating the mean entropy and the mean mu-tual entropy defined by the classical dynamical entropy (Kolmogorov-Sinai). The quan-tum dynamical entropy was first studied by Emch [13] and Connes-Stormer [11]. Afterthat, several approaches for introducing the quantum dynamical entropy were proposed[10, 3, 8, 39, 15, 44, 9, 27, 28, 2, 19, 45]. The efficiency of information transmission for thequantum processes is investigated by using the von Neumann entropy [22] and the Ohyamutual entropy [24]. These entropies were extended to S-mixing entropy by Ohya [26, 27] ingeneral quantum systems. The mean entropy and the mean mutual entropy for the quantumdynamical systems were introduced based on the S-mixing entropy. In this paper, basedon research into the dynamical entropy and mean mutual entropy of quantum systems,this study investigates the characteristics of quantum channels that exhibit entanglement,a property unique to quantum systems, and investigates the behaviour of quantum entropyfor compound quantum channels by changing the perspective from information transmis-sion between input and output to a new perspective of information transmission from theinitial state to the final state.
The requirement of complete positivity is very often regarded as a fundamental consistency condition for the description of open quantum dynamics. We critically examine this requirement and discuss both its physical motivations and its limitations. We analyse proposals based on restricting the domain of non-completely positive maps to subsets of compatible initial states. Using isotropic states as a concrete example, we show that such domain restrictions become increasingly severe with growing system dimension, revealing an intrinsic weakness of the compatibility-based approach.
Quantum indistinguishability of non-orthogonal quantum states is a valuable resource in quantum information applications such as cryptography and randomness generation. In this article, we present a sequential state-discrimination scheme that enables multiple parties to share quantum uncertainty, in terms of the max relative entropy, generated by a single party. Our scheme is based upon maximum-confidence measurements and takes advantages of weak measurements to allow a number of parties to perform state discrimination on a single quantum system. We review known sequential state discrimination and show how our scheme would work through a number of examples where ensembles may or may not contain symmetries. Our results will have a role to play in understanding the ultimate limits of sequential information extraction and guide the development of quantum resource sharing in sequential settings.
