The notion of Quantum Universe as the whole world obeying the rules of Quantum Physics is in deep conflict with the statistical interpretation of Quantum Mechanics. The latter emerged as the dynamamical theory of microscopic, in principle invisible world. Its statistical interpretation is the only possibility which is consistent with the macroscopic experimental data about this world, the only visible things in our single but partially hidden universe. By definition, the Universe is a unique whole of as many parts, branches or worlds as one could wish to have a more comprehensive picture for the invisible part of the Universe. There is no reality in a mixed state for the whole universe, a statistical ensemble, corresponding to a mixture of the pure states for the whole universe is a nonsense: Any ensemble of the worlds is a new world which must be included into the Universe of the whole world. Quantum Reality, identified with a pure Quantum State, may not determine measurement events, but at least it determines quantum potentiality, i.e. propensity of all quantum properties, or propositions, as well as probabilities of all observable events. However these events, if they all were observed, completely determine this reality, otherwise the Universe would emerge in a mixed state. Any mixed state of the Universe is nothing but a unique mixture of the undertermined realities in the result of the loss of unobserved Quantum Information.
The oservable events, the only things which matter, correspond to macroscopically verifiable properties (propositions) composing a Boolean algebra. The events, as the elements of the reality, must be compatible with every proposition about a quantum property, but unlike in the classical case, not all quantum propositions have this compatibility property. They must be causal, but nondemolition for the invisible quantum world, making it predictable at least in the result of a statistical inference. Unfortunately in the orthodox quantum theory of only quantum (i.e. microscopic) world there is no place for such events. The new quantum causality postulate, mathematically defining the events and the hypothetical Bell's beables as the nondemolition (i.e. central) observables in an extended quantum theory, is called the Nondemolition Principle [1]. All paradoxes of the probabilistic interpretation of quantum theory arise from incompleteness of the conventional quantum mechanics for the dynamical description of this quantum causality that quantum reality should result from the events, not only from an initial state. The microscopic world is incomplete without the classical world: there is no place for the causal events except the trivial ones 0 and 1in the microscopic, purely quantum world which would condition any quantum state on the operator algebra of a purely quantum system.
Von Neumann and then Schroedinger tried hard to extend the "new" reversible quantum mechanics emerged in the 1925, in a way that it would be consistent with the irreversible events, like quantum decays and quantum jumps, of the "old" one such that the predictability of the microscopic quantum dynamics would be restored at least in the decribed above weak sense of quantum causality, and therefore could explain quantum decoherence due the measurement. However all the quantum mechanical extensions, which would include the macroscopic measurement apparatus into the rest of the universe as a part of the combined reversible Hamiltonian system as it was suggested by Bohr, failed due to the nonexistence of the reversible micro-macro (or quantum-classical) potential interaction. Thus the classical idea of the Hamiltonian time-reflectional symmetry, which has been experimentally confirmed only for cosmologically short time-intervals of our life but contradicts to the recent cosmological data about the origin of the universe (Big Bang), didn't allow to explore the only remaining, time-asymmetric possibility of the extension of quantum mechanics. This nonexistence of events in time symmetric quantum mechanics and its inconsistency with quantum causality remains a source of the paradoxes even in the "consistent" phenomenological irreversible quantum theories with trajectories or histories without their dynamical derivation and quantum-mechanical interpretation.
It is a time-asymmetric dynamics of the event enhanced quantum mechanics which includes all phenomenological (non Hamiltonian) reduction theories such as von Neumann projection postulate and continuous reduction, quantum state jumps and spontaneous localization theory, quantum state diffusion and quantum continuous trajectories. The corresponding basic equations, which are stochastic (filtering) generalizations of the Schroedinger and von Neumann equations, were first derived by Belavkin during the 80's (see the QEE and QFC pages) from the unitary interaction models for time-continuous non-demolition quantum measurements. These dynamical models are the interaction representation models for the pure, Hamiltonian information dynamics of an extended system in which there is a place for the causal events and Bell's beables. They simply compose the center of a reducible algebra of all potential observables, including the macroscopic, non demolition quantum measurements. The quantum future meets the classical past in our world as the present boundary in this event enhanced mechanical theory.
The crucial point of QEM is that the invertible Heisenberg dynamics, induced on the decomposable algebra by the corresponding unitary evolution in an extended Hilbert space, is irreversible, continuously reducing this algebra. Due to this some, initially pure, states may become identical and even mixed over the center of this algebra if no statistical inference is made, or at least not all events are actually recorded. We call this new, time-asymmetric Hamiltonian event-enhanced quantum mechanics the Quantum Event-Mechanics, or shortly the Eventum Mechanics. It explains how the Decoherence and Information may dynamically emerge in the extended quantum mechanics as the result of an ignorance of the events or their filtering from a pure initial state. It also brings a new, nonclassical interpretation for the usual, classical probability measure of the visible, macroscopic events as purely dynamically emerging chaos which is not due to the instability or incompleteness of the dynamical description and initial state, but due to the Hamiltonian interaction with the invisible, microscopic world. Thus, the Quantum Event-Mechanics is a time asymmetric Hamiltonian theory of visible and hidden variables which explains all classical paradoxes of quantum theory in explicit terms of mathematically solvable models containing events and satisfying causality.
It was von Neumann who first proved that Quantum Probability is intrinsic for the mathematical formulation of Quantum Theory as Hilbert space operator theory with the expectations as the statistical states. Even the Bell's infamous example of a hidden classical variable, which is impossible in any but not the exceptional two dimensional space, does not contradict von Neumann's theorem, because his hidden variable does not satisfy the tensor product compositional principle. As it was proven in [2], this simply follows from the Gleason's theorem supplemented by this Quantum Composition Principle. The infamous hidden variable theories tried hard to explain the `visible' quantum world by a 'hidden' classical, but they all have failed due to this reason. The Eventum Mechanics, in contrast, explains the quantum phenomenology of the visible events by simple and honest declaration of the existance of two worlds: the visible part of the universe is macroscopic, or classical world, and the quantum, microscopic world, although indirectly observed, will always remain hidden. In this sense it is the only mathematically consistent theory with Copenhagen interpretation. The time arrow in Quantum Event-Mechanics is kinematicly irreversible, since quantum part of the Universe cannot be moved by any Heisenberg dynamics into the quantum which is opposit direction for Eventum Mechanics motion. What was visible is the past, composes classical reality, and what was hidden is the future, remains quantum potentiality in due course of this motion. More about this and the mathematical models of information dynamics and boundary value problems of eventum mechanics one can find in the review paper [2], see also [3].