Related papers: Structure of completely positive quantum master eq…
We identify two broad types of noninvertibilities in quantum dynamical maps, one necessarily associated with CP indivisibility and one not so. We study the production of (non-)Markovian, invertible maps by the process of mixing…
Quantum dynamical maps provide suitable mathematical representation of quantum evolutions. It is the very notion of complete positivity which provides a proper mathematical representation of quantum evolution and gives rise to the powerful…
We discuss the conceptually different definitions used for the non-Markovianity of classical and quantum processes. The well-established definition for non-Markovianity of a classical stochastic process represents a condition on the…
The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master…
We introduce a general construction of master equations with memory kernel whose solutions are given by completely positive trace preserving maps. These dynamics going beyond the Lindblad paradigm are obtained with reference to classical…
Do phenomenological master equations with memory kernel always describe a non-Markovian quantum dynamics characterized by reverse flow of information? Is the integration over the past states of the system an unmistakable signature of…
We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by…
A systematic approach to the non-Markovian quantum dynamics of open systems is given by the projection operator techniques of nonequilibrium statistical mechanics. Combining these methods with concepts from quantum information theory and…
In this paper, we analyze the evolution of the generalized Pauli channels governed by the memory kernel master equation. We provide necessary and sufficient conditions for the memory kernel to give rise to the legitimate (completely…
During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse set of research communities. This interest has arisen due to fundamental problematics how to…
Non-Markovian processes may arise in physics due to memory effects of environmental degrees of freedom. For quantum non-Markovianity, it is an ongoing debate to clarify whether such memory effects have a verifiable quantum origin, or…
We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which…
Non-Markovian local in time master equations give a relatively simple way to describe the dynamics of open quantum systems with memory effects. Despite their simple form, there are still many misunderstandings related to the physical…
The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex…
A semi-Markov process method for obtaining general counting statistics for open quantum systems is extended to the scenario of resetting. The simultaneous presence of random resets and wave function collapses means that the quantum jump…
Markov processes play an important role in physics and the theory of open systems in particular. In this paper we study the asymptotic evolution of trace-nonincreasing homogenous quantum Markov processes (both types, discrete quantum Markov…
The quantum master equation (QME), used to describe the Markov process of interaction between atoms and field, has a number of significant drawbacks. It is extremely memory intensive, and also inapplicable to the case of long-term memory in…
Investigations of quantum and mesoscopic thermodynamics force one to answer two fundamental questions associated with the foundations of statistical mechanics: (i) how does macroscopic irreversibility emerge from microscopic reversibility?…
We study the concepts of complete positivity, positivity and non-Markovianity in a two-level open quantum system whose dynamics are governed by a time-local quantum master equation. We establish necessary and sufficient conditions on the…
Recent developments in practical quantum engineering and control techniques have allowed significant developments for experimental studies of open quantum systems and decoherence engineering. Indeed, it has become possible to test…