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The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated…
Quantum Metrology Triangle experiments combine three quantum electrical effects (the Josephson effect, the quantum Hall effect and the single-electron transport effect) used in metrology. These experiments allow important fundamental…
We consider an application of the mathematical formalism of quantum mechanics (QM) outside physics, namely, to game theory. We present a simple game between macroscopic players, say Alice and Bob (or in a more complex form - Alice, Bob and…
Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits…
Quantum physics, which describes the strange behavior of light and matter at the smallest scales, is one of the most successful descriptions of reality, yet it is notoriously inaccessible. Here we provide an approachable explanation of…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…
We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like interference pattern could appear as a statistical…
In spite of the fact that statistical predictions of quantum theory (QT) can only be tested if large amount of data is available a claim has been made that QT provides the most complete description of an individual physical system.…
We consider a macroscopic quantum system in a tilted double-well potential. By solving Hamiltonian equation, we obtain tunneling probabilities which contain oscillation effects. To show how one can decide between quantum mechanics and the…
Jeffreys-Lindley paradox is a case where frequentist and Bayesian hypothesis testing methodologies contradict with each other. This has caused confusion among data analysts for selecting a methodology for their statistical inference tasks.…
The properties of quantum information in space-time can be investigated by studying operational tasks. In one such task, summoning, an unknown quantum state is supplied at one point, and a call is made at another for it to be returned at a…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
The Prisoner's Dilemma game (PDG) is one of the simple test-beds for the probabilistic nature of the human decision-making process. Behavioral experiments have been conducted on this game for decades and show a violation of the so-called…
Odds ratios and log-linear parameters are not collapsible, meaning that including a variable into the analysis or omitting one from it, may change the strength of association among the remaining variables. Even the direction of association…
The phenomenon of universality is one of the most striking in many-body physics. Despite having sometimes wildly different microscopic constituents, systems can nonetheless behave in precisely the same way, with only the variable names…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
We suggest a somewhat non-standard view on a set of curious, paradoxical from the standpoint of simple classical physics and everyday experience phenomena. There are the quantisation (discrete set of values) of the observables (e.g.,…
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
It is well-known that the set of statistics that can be observed in a Bell-type experiment is limited by quantum theory. Unfortunately, tools are missing to identify the precise boundary of this set. Here, we propose to study the set of…
We establish a sharp quantum advantage in determining the parity (even/odd) of an unknown permutation applied to any number $n \ge 3$ of particles. Classically, this is impossible with fewer than $n$ labels, being that the success is…