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The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating…
We enhance the standard formalism of quantum theory to enable events. The concepts of experiment and of measurement are defined. Dynamics is given by Liouville's equation that couples quantum system to a classical one. It implies a unique…
It is shown that piecewise deterministic dissipative quantum dynamics in a vector space with indefinite metric can lead to well defined, positive probabilities. The case of quantum jumps on the Poincar'e disk is studied in details,…
Time plays a special role in Standard Quantum Theory. The concept of time observable causes many controversies there. In Event Enhanced Quantum Theory (in short: EEQT) Schroedinger's differential equation is replaced by a em piecewise…
We review what we call "event-enhanced formalism" of quantum theory. In this approach we explicitly assume classical nature of events. Given a quantum system, that is coupled to a classical one by a suitable coupling, classical events are…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
We prove that, contrary to the standard quantum theory of continuous observation, in the formalism of Event Enhanced Quantum Theory the stochastic process generating individual sample histories of pairs (observed quantum system, observing…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of…
In sections 1 and 2 we review Event Enhanced Quantum Theory (EEQT). In section 3 we discuss applications of EEQT to tunneling time, and compare its quantitative predictions with other approaches, in particular with B\"uttiker-Larmor and…
A fundamental question in the debate about the interpretations of quantum mechanics (QM) is whether the universe is fundamentally deterministic or fundamentally probabilistic. This self-contained paper shows for a microsystem made up of a…
Stochastic quantum trajectories, such as pure state evolutions under unitary dynamics and random measurements, offer a crucial ensemble description of many-body open system dynamics. Recent studies have highlighted that individual quantum…
In this paper, we develop a formalism describing in a relativistic way a system which consists of a classical and a quantum part being coupled. The formalism models one particle with spin 1/2 and it is a possible relativistic extension of…
As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial…
Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
The probabilistic interpretation of quantum mechanics has been a point of discussion since the earliest days of the theory. The development of quantum technologies transfer these discussions from philosophical interest to practical…
Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared…
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the…
Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing…