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This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
While spatial quantum correlations have been studied in great detail, much less is known about the genuine quantum correlations that can be exhibited by temporal processes. Employing the quantum comb formalism, processes in time can be…
Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the…
A non-Markovianity measure for quantum channels is introduced based on causality measure - a monotone of causal (temporal) correlations - arising out of the pseudo-density matrix (PDM) formalism which treats quantum correlations in space…
Markovianity lies at the heart of communication problems. This in turn makes the information-theoretic characterization of Markov processes worthwhile. Data processing inequalities are ubiquitous in this sense, assigning necessary…
Tensors and traceouts are generalised, so that systems can be partitioned according to almost arbitrary logical predicates. One might have feared that the familiar interrelations between the notions of unitarity, complete positivity,…
The time reversal of a completely-positive, nonequilibrium discrete-time quantum Markov evolution is derived via a suitable adjointness relation. Space-time harmonic processes are introduced for the forward and reverse-time transition…
Stochastic (Markovian) process algebra extend classical process algebra with probabilistic exponentially distributed time durations denoted by rates (the parameter of the exponential distribution). Defining a semantics for such an algebra,…
This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…
We consider a two-dimensional quantum control system evolving under an entropy-increasing irreversible dynamics in the semigroup form. Considering a phenomenological approach to the dynamics, we show that the accessibility property of the…
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…
Using the age-structure formalism, we definitely establish connections between semi-Markov processes and the dynamics of open quantum systems that satisfy the Markov quantum master equations. A generalized Feynman-Kac formula of the…
The problem of recognizing (non-)Markovianity of a quantum dynamics is revisited through analyzing quantum correlations. We argue that instantaneously-vanishing quantum discord provides a necessary and sufficient condition for Markovianity…
We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…
The dynamics of an open quantum system can be described by a quantum operation, a linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to…
A new notion of stochastic germs for quantum processes is introduced and a characterisation of the stochastic differentials for positive definite (PD) processes is found in terms of their germs for arbitrary Ito algebra. A representation…
We demonstrate that any Euclidean-time quantum mechanical theory may be represented as a neural network, ensured by the Kosambi-Karhunen-Lo\`eve theorem, mean-square path continuity, and finite two-point functions. The additional constraint…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
We discuss fundamental features of the local expression for the entropy production rate of the nonequilibrium quantum dynamics of open systems and its relations to memory effects and the spectrum of the generator of the dynamics. Defining…
In the theory of testing for Markovian processes developed so far, exponentially timed internal actions are not admitted within processes. When present, these actions cannot be abstracted away, because their execution takes a nonzero amount…