Related papers: Structure of completely positive quantum master eq…
Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic…
We investigate the problem of simulating classical stochastic processes through quantum dynamics, and present three scenarios where memory or time quantum advantages arise. First, by introducing and analysing a quantum version of the…
The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered.…
We consider a class of semi-Markov processes (SMP) such that the embedded discrete time Markov chain may be non-homogeneous. The corresponding augmented processes are represented as semi-martingales using stochastic integral equation…
We propose to use the quantum Fisher information in characterizing the information flow of open quantum systems. This information-theoretic approach provides a quantitative measure to statistically distinguish Markovian and non-Markovian…
We discuss in detail how non-Markovian open system dynamics can be described in terms of quantum jumps [J. Piilo et al., Phys. Rev. Lett. 100, 180402 (2008)]. Our results demonstrate that it is possible to have a jump description contained…
Non-Markovian reduced dynamics of an open system is investigated. In the case the initial state of the reservoir is the vacuum state, an approximation is introduced which makes possible to construct a reduced dynamics which is completely…
Master equations describing open quantum dynamics are typically first order differential equations. When such dynamics brings the trajectories in state space of more than one initial state to the same point at finite instants in time, the…
We point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time…
Although quantum coherence is a basic trait of quantum mechanics, the presence of coherences in the quantum description of a certain phenomenon does not rule out the possibility to give an alternative description of the same phenomenon in…
Markov processes are widely used in modeling random phenomena/problems. However, they may not be adequate in some cases where more general processes are needed. The conditionally Markov (CM) process is a generalization of the Markov process…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly…
We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the…
We study the Classical Probability analogue of the dilations of a quantum dynamical semigroup in Quantum Probability. Given a (not necessarily homogeneous) Markov chain in discrete time in a finite state space E, we introduce a second…
Memory effects in the dynamics of open systems have been the subject of significant interest in the last decades. The methods involved in quantifying this effect, however, are often difficult to compute and may lack analytical insight. With…
We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing,…
Markovian master equations (formally known as quantum dynamical semigroups) can be used to describe the evolution of a quantum state $\rho$ when in contact with a memoryless thermal bath. This approach has had much success in describing the…
We study the open dynamics of a quantum two-level system coupled to an environment modeled by random matrices. Using the quantum channel formalism, we investigate different quantum Markovianity measures and criteria. A thorough analysis of…
Open quantum systems exhibit a rich phenomenology, in comparison to closed quantum systems that evolve unitarily according to the Schr\"odinger equation. The dynamics of an open quantum system are typically classified into Markovian and…