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In previous research, we showed that 'texts that tell a story' exhibit a statistical structure that is not Maxwell-Boltzmann but Bose-Einstein. Our explanation is that this is due to the presence of 'indistinguishability' in human language…
Quantum entanglement, perhaps the most non-classical manifestation of quantum information theory, cannot be used to transmit information between remote parties. Yet, it can be used to reduce the amount of communication required to process a…
No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no-go arguments against non-contextual hidden variables. All such arguments rely on choosing special sets of quantum-mechanical…
The Heisenberg double of a Hopf algebra may be regarded as a quantum analogue of the cotangent bundle of a Lie group. Quantum duality principle describes relations between a Hopf algebra, its dual, and their Heisenberg double in a way which…
Developing a better understanding of surprising or counterintuitive phenomena has constituted a significant portion of deep learning research in recent years. These include double descent, grokking, and the lottery ticket hypothesis --…
We describe quantum tomography as an inverse statistical problem and show how entropy methods can be used to study the behaviour of sieved maximum likelihood estimators. There remain many open problems, and a main purpose of the paper is to…
The Copenhagen Interpretation describes individual systems, using the same Hilbert space formalism as does the statistical ensemble interpretation (SQM). This leads to the well-known paradoxes surrounding the Measurement Problem. We extend…
Recently we proposed measurement theory (i.e., quantum language, or the linguistic interpretation of quantum mechanics), which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. This turn from…
A suggestion for an observational test of the difference between quantum mechanics and noncontextual hidden variables theories requires the measurement of a product of two commuting observables without measuring either observable…
The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes…
Human judgments of word similarity have been a popular method of evaluating the quality of word embedding. But it fails to measure the geometry properties such as asymmetry. For example, it is more natural to say "Ellipses are like Circles"…
At present, there are two possible, and equally plausible, explanations for the physics of quantum measurement. The first explanation, known as the many-worlds interpretation, does not require any modification of quantum mechanics, and…
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for…
Based on ideas of quantum theory of open systems and psychological dual system theory we propose two novel versions of Non-Boolean logic. The first version can be interpreted in our opinion as simplified description of primitive…
By using the abstract structures investigated in the first Part of this article, we develop a semantics for an epistemic language, which expresses sentences like "Alice knows that Bob does not understand that PI is irrational". One is…
A solution to the second measurement problem, determining what prior microscopic properties can be inferred from measurement outcomes ("pointer positions"), is worked out for projective and generalized (POVM) measurements, using consistent…
We present a new and feasible test proving quantum contextuality in four-dimensional Hiltbert space. In our scheme, a contradiction between quantum mechanics and noncontextual hidden variables is revealed through the measurement statistics…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
We consider the classical correlations that two observers can extract by measurements on a bipartite quantum state, and we discuss how they are related to the quantum mutual information of the state. We show with several examples how…
I will propose that the reality to which the quantum formalism implicitly refers is a kind of generalized history, the word history having here the same meaning as in the phrase sum-over-histories. This proposal confers a certain…