Related papers: On the quantum principles of cognitive learning
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
In the quantum Bayesian (or QBist) conception of quantum theory, "quantum measurement" is understood not as a comparison of something pre-existent with a standard, but instead indicative of the creation of something new in the universe:…
We propose an alternative and unifying framework for decision-making that, by using quantum mechanics, provides more generalised cognitive and decision models with the ability to represent more information than classical models. This…
Quantitative characterizations and estimations of uncertainty are of fundamental importance in optimization and decision-making processes. Herein, we propose intuitive scores, which we call certainty and doubt, that can be used in both a…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
We are investigating cognitive issues in learning quantum mechanics in order to develop effective teaching and learning tools. The analysis of cognitive issues is particularly important for bridging the gap between the quantitative and…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
In the Quantum-Bayesian interpretation of quantum theory (or QBism), the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In…
This article may be seen as a summary and a final discussion of the work that the author has done in recent years on the foundation of quantum theory. It is shown that quantum mechanics as a model follows under certain specific conditions…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…
This paper presents a framework for Quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…
The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean subset logic is usually mis-specified as the special case of…
In studies of entanglement, finding out if a state is entangled and quantifying the amount of entanglement contained in a state are related but different questions. Similarly in studies of causality, finding out the causal structures…
In this brief note I argue that putting conscious observers at the center of the considerations clarifies and strengthens the many-worlds interpretation. The basic assumption, which seems extremely plausible based on our current…
The ideas of Sensible Quantum Mechanics are expressed in lay terms for philosophers of consciousness and others. A framework is proposed and explained for the `psycho-physical-parallelism' between conscious experiences and the mathematical…
While a positive operator valued measure gives the probabilities in a quantum measurement, an instrument gives both the probabilities and the a posteriori states. By interpreting the instrument as a quantum channel and by using the…
Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…
The subjective Bayesian interpretation of probability asserts that the rules of the probability calculus follow from the normative principle of Dutch-book coherence: A decision-making agent should not assign probabilities such that a series…