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We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold -- these…
Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…
In this paper we derive the complex Hilbert space formalism of quantum theory from four simple information theoretic axioms. It is shown that quantum theory is the only non classical probabilistic theory satisfying the following axioms:…
In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…
We consider how to define a natural probability distribution over worlds within a simple class of deterministic many-worlds theories. This can help us understand the typical properties of worlds within such states, and hence explain the…
The quantum-mechanical rule for probabilities, in its most general form of positive-operator valued measure (POVM), is shown to be a consequence of the environment-assisted invariance (envariance) idea suggested by Zurek [Phys. Rev. Lett.…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
The scientific community is becoming more and more interested in the research that applies the mathematical formalism of quantum theory to model human decision-making. In this paper, we provide the theoretical foundations of the quantum…
The lately developed part of Quantum Bayesianism named QBism has been proclaimed by its authors a powerful interpretation of Quantum Physics. This article presents analysis of some aspects of QBism. The considered examples show…
We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical…
Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
I flesh out the sense in which the informational approach to interpreting quantum mechanics, as defended by Pitowsky and Bub and lately by a number of other authors, is (neo-)Bohrian. I argue that on this approach, quantum mechanics…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
We present the fundamentals of the quantum theoretical approach we have developed in the last decade to model cognitive phenomena that resisted modeling by means of classical logical and probabilistic structures, like Boolean, Kolmogorovian…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
Quantum mechanics traditionally places the observer outside of the system being studied and employs the Born interpretation. In this and related papers the observer is placed inside the system. To accomplish this, special rules are required…
Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…
QBism is a novel interpretation of quantum mechanics. With its radical emphasis on the subject, QBism provides a welcome corrective to popular misrepresentations of the epistemological reflections of Niels Bohr, while Bohr, rightly…