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An extension of the Born rule, the {\it quantum typicality rule}, has recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into…
We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest…
In this article, we study an opposite problem of universal quantum state comparison, that is unambiguous determining whether multiple unknown quantum states from a Hilbert space are orthogonal or not. We show that no unambiguous quantum…
There are two main opposing schools of statistical reasoning, Frequentist and Bayesian approaches. Until recent days, the frequentist or classical approach has dominated the scientific research, but Bayesianism has reappeared with a strong…
Bayesian networks and their accompanying graphical models are widely used for prediction and analysis across many disciplines. We will reformulate these in terms of linear maps. This reformulation will suggest a natural extension, which we…
In this presentation, I argue that weak measurements empirically support the notion of quantum superpositions as statistical alternatives. In short, weak measurements show that Schroedinger's cat is already dead or alive before the…
From the ancient Einstein-Podolsky-Rosen paradox to the recent Sorkin-type impossible measurements problem, the contradictions between relativistic causality, quantum non-locality, and quantum measurement have persisted. Based on quantum…
Quantum paradoxes show that the outcomes of different quantum measurements cannot be described by a single measurement-independent reality. Any theoretical description of a quantum measurement implies the selection of a specific measurement…
The notorious quantum measurement problem brings out the difficulty to reconcile two quantum postulates: the unitary evolution of closed quantum systems and the wave-function collapse after a measurement. This problematics is particularly…
We have studied the possibility of post-quantum theories more nonlocal than the (standard) quantum theory using the modification of the quantum probability rule under the no-signaling condition. For this purpose we have considered the…
The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing…
Motivated by some recent news, a journalist asks a group of physicists: "What's the meaning of the violation of Bell's inequality?" One physicist answers: "It means that non-locality is an established fact". Another says: "There is no…
A lively ongoing debate is taking place, since the extraordinary emergence of Large Language Models (LLMs) with regards to their capability to understand the world and capture the meaning of the dialogues in which they are involved.…
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of…
It is shown that in two-state quantum theory, a generic quantum state can be described by a non-computable real number. In terms of this, the criterion for measurement outcome is simply and deterministically defined. This demonstration is…
We analyze the logical foundations of quantum mechanics (QM) by stressing non-objectivity of quantum observables which is a consequence of the absence of logical atoms in QM. We argue that the matter of quantum non-objectivity is that, on…
Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
The ability to calculate precise likelihood ratios is fundamental to many STEM areas, such as decision-making theory, biomedical science, and engineering. However, there is no assumption-free statistical methodology to achieve this. For…
A PhD student is locked inside a box, imitating a quantum system by mimicking the measurement statistics of any viable observable nominated by external observers. Inside a second box lies a genuine quantum system. Either box can be used to…