Related papers: A quantum version of randomization criterion
The quantum mechanical probability densities are compared with the probability densities treated by the theory of random variables. The relevance of their difference for the interpretation of quantum mechanics is commented.
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
The meaning of randomization tests has become obscure in statistics education and practice over the last century. This article makes a fresh attempt at rectifying this core concept of statistics. A new term -- "quasi-randomization test" --…
We give a tutorial exposition of the analogue of the filtering equation for quantum systems focusing on the quantum probabilistic framework and developing the ideas from the classical theory. Quantum covariances and conditional expectations…
We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized…
We give a general overview of various flavors of the equivalence principle in classical and quantum physics, with special emphasis on the so-called weak equivalence principle, and contrast its validity in mechanics versus field theory. We…
We present an experimental illustration on the quantum sensitivity of decision making machinery. In the decision making process, we consider the role of available information, say hint, whether it influences the optimal choices. To the end,…
From a quantum information perspective, verifying quantum coherence in a quantum experiment typically requires adjusting measurement settings or changing inputs. A paradigmatic example is that of a double-slit experiment, where observing…
We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels…
Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities---this is the conjunction fallacy. One of the most discussed accounts of this…
We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and…
Some quantal systems require only a small part of the full quantum theory for their analysis in classical terms. In such understanding we review some recent literature on semiclassical treatments. An analysis of it allows one to see that…
In this paper, inspired by the "Minimum Description Length Principle" in classical Statistics, we introduce a new method for predicting the outcomes of a quantum measurement and for estimating the state of a quantum system with minimum…
We present a general theory of comparison of quantum channels, concerning with the question of simulability or approximate simulability of a given quantum channel by allowed transformations of another given channel. We introduce a…
A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding…
With the slow but constant progress in the coherent control of quantum systems, it is now possible to create large quantum superpositions. There has therefore been an increased interest in quantifying any claims of macroscopicity. We…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
Lately, so-called "quantum" models, based on parts of the mathematics of quantum mechanics, have been developed in decision theory and cognitive sciences to account for seemingly irrational or paradoxical human judgments. We consider here…
Quantum annealing is a generic algorithm using quantum-mechanical fluctuations to search for the solution of an optimization problem. The present paper first reviews the fundamentals of quantum annealing and then reports on preliminary…
Quantum decision systems are being increasingly considered for use in artificial intelligence applications. Classical and quantum nodes can be distinguished based on certain correlations in their states. This paper investigates some…