Related papers: Identifying Quantum Structures in the Ellsberg Par…
We provide an overview of the results we have attained in the last decade on the identification of quantum structures in cognition and, more specifically, in the formalization and representation of natural concepts. We firstly discuss the…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
Why does such a successful theory like Quantum Mechanics have so many mysteries? The history of this theory is replete with dubious interpretations and controversies, and yet a knowledge of its predictions, however, contributed to the…
Contextuality, the impossibility of assigning a single random variable to represent the outcomes of the same measurement procedure under different experimental conditions, is a central aspect of quantum mechanics. Thus defined, it appears…
Quantum mechanics (QM) has attracted a considerable amount of mysticism, in public opinion and even among academic researches, due to some of its conceptually puzzling features, such as the modification of reality by the observer and…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…
The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of…
Quantum effects and, in particular, entanglement are by now widely recognized in all areas of physics and related fields. However, we feel that the precise notion of entanglement---though mathematically well-defined---still generates…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent discipline called Quantum Cognition. These principles have been applied to…
An overview of the conceptuality interpretation of quantum mechanics is presented, along with an explanation of how it sheds light on key quantum and relativistic phenomena. In particular, we show how the interpretation clarifies…
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the…
Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics…
The coexistence relation of quantum effects is a fundamental structure, describing those pairs of experimental events that can be implemented in a single setup. Only in the simplest case of qubit effects an analytic characterization of…
We introduce a logic modelling some aspects of the behaviour of the measurement process, in such a way that no direct mention of quantum states is made, thus avoiding the problems associated to this rather evasive notion. We then study some…
A different approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible to assign numerical…
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 explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…