Entanglement of Conceptual Entities in Quantum Model Theory (QMod)

We have recently elaborated 'Quantum Model Theory' (QMod) to model situations where the quantum effects of contextuality, interference, superposition, entanglement and emergence, appear without the entities giving rise to these situations having necessarily to be of microscopic nature. We have shown that QMod models without introducing linearity for the set of the states. In this paper we prove that QMod, although not using linearity for the state space, provides a method of identification for entangled states and an intuitive explanation for their occurrence. We illustrate this method for entanglement identification with concrete examples

Quantum Model Theory (QMod): Modeling Contextual Emergent Entangled Interfering Entities

In this paper we present 'Quantum Model Theory' (QMod), a theory we developed to model entities that entail the typical quantum effects of 'contextuality', 'superposition', 'interference', 'entanglement' and 'emergence'. The aim of QMod is to put forward a theoretical framework that is more general than standard quantum mechanics, in the sense that, for its complex version it only uses this quantum calculus locally, i.e. for each context corresponding to a measurement, and for its real version it does not need the property of 'linearity of the set of states' to model the quantum effect. In this sense, QMod is a generalization of quantum mechanics, similar to how the general relativity manifold mathematical formalism is a generalization of special relativity. We prove by means of a representation theorem that QMod can be used for any entity entailing the typical quantum effects mentioned above. Some examples of application of QMod in concept theory and macroscopic physics are also considered.Comment: 1 figur

"Potentialities or Possibilities": Towards Quantum Information Science?

The use of quantum concepts and formalisms in the information sciences is assessed through an analysis of published literature. Five categories are identified: use of loose analogies and metaphors between concepts in quantum physics and library/information science; use of quantum concepts and formalisms in information retrieval; use of quantum concepts and formalisms in studying meaning and concepts; quantum social science, in areas adjacent to information science; and the qualitative application of quantum concepts in the information disciplines. Quantum issues have led to demonstrable progress in information retrieval and semantic modelling, with less clear-cut progress elsewhere. Whether there may be a future “quantum turn” in the information sciences is debated, the implications of such a turn are considered, and a research agenda outlined

The Unreasonable Success of Quantum Probability I: Quantum Measurements as Uniform Fluctuations

We introduce a 'uniform tension-reduction' (UTR) model, which allows to represent the probabilities associated with an arbitrary measurement situation and use it to explain the emergence of quantum probabilities (the Born rule) as 'uniform' fluctuations on this measurement situation. The model exploits the geometry of simplexes to represent the states, in a way that the measurement probabilities can be derived as the 'Lebesgue measure' of suitably defined convex subregions of the simplexes. We consider a very simple and evocative physical realization of the abstract model, using a material point particle which is acted upon by elastic membranes, which by breaking and collapsing produce the different possible outcomes. This easy to visualize mechanical realization allows one to gain considerable insight into the possible hidden structure of an arbitrary measurement process. We also show that the UTR-model can be further generalized into a 'general tension-reduction' (GTR) model, describing conditions of lack of knowledge generated by 'non-uniform' fluctuations. In this ampler framework, particularly suitable to describe experiments in cognitive science, we define and motivate a notion of 'universal measurement', describing the most general possible condition of lack of knowledge in a measurement, emphasizing that the uniform fluctuations characterizing quantum measurements can also be understood as an average over all possible forms of non-uniform fluctuations which can be actualized in a measurement context. This means that the Born rule of quantum mechanics can be understood as a first order approximation of a more general non-uniform theory, thus explaining part of the great success of quantum probability in the description of different domains of reality. This is the first part of a two-part article.Comment: 50 pages, 10 figure

A Hilbert Space Geometric Representation of Shared Awareness and Joint Decision Making

Two people in the same situation may ascribe very different meanings to their experiences. They will form different awareness, reacting differently to shared information. Various factors can give rise to this behavior. These factors include, but are not limited to, prior knowledge, training, biases, cultural factors, social factors, team vs. individual context, time, resources, and technology. At the individual level, the differences in attaining separate actions by accessing shared information may not be considered as an anomaly from the perspective of rational decision-making. But for group behavior, reacting differently to the shared information can give rise to conflicts and deviations from an expected behavior, and are categorized as an anomaly or irrational behavior. The lack of proper recognition of the reasons for differences can even impede the shared action towards attaining a common objective. The manifestation of differences becomes noticeable in complex situations. The shared awareness approaches that originate from available situational awareness models fail to recognize the reasons of an unexpected decision in these situations. One reason for this is that in complex situations, incompatible events can become dominant. Human information processing is sensitive to the compatibility of the events. This, and various other human psychological characteristics, require models to be developed that include comprehensive formalisms for both compatible and incompatible events in complex situations. Quantum probability provides a geometrical probabilistic formalism to study the decision and the dynamic cognitive systems in complex situations. The event representation in Hilbert space provides the necessary foundation to represent an individual\u27s knowledge of a situation. Hilbert space allows representing awareness as a superposition of indefinite states. These states form a complete N-dimensional Hilbert space. Within the space generated, events are represented as a subspace. By using these characteristics of Hilbert space and quantum geometrical probabilities, this study introduces a representation of self and other-than-self in a situation. An area of awareness with the possibility of projection onto the same event allows representing shared awareness geometrically. This formalism provides a coherent explanation of shared awareness for both compatible and incompatible events. Also, by using the superposition principles, the dissertation introduces spooky action at a distance concept in studying shared awareness