Related papers: Born's rule from almost nothing
The physical meaning of weak values and measurements can be completely understood with Born rule and the general probability theory. It is known that the weak value of an observable $\hat A$ with post-selection $\langle F|$ may be out of…
As it is known, Gleason's theorem is not applicable for a two-dimensional Hilbert space since in this situation Gleason's axioms are not strong enough to imply Born's rule thus leaving room for a dispersion-free probability measure i.e.,…
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…
Let $X$ be the sum of a fractional Brownian motion with Hurst parameter $H$ and an absolutely continuous and adapted drift process. We establish a simple criterion that guarantees that the law of $X$ is absolutely continuous with respect to…
The law of total probability may be deployed in binary classification exercises to estimate the unconditional class probabilities if the class proportions in the training set are not representative of the population class proportions. We…
One more derivation of the quantum probability rule is presented in order to shed more light on the versatile aspects of this fundamental law. It is shown that the change of state in minimal quantum non-demolition measurement, also known as…
Simple necessary and sufficient conditions for a $n$-tuple of noncommutative polynomials to be a cyclic gradient are given and similarly for a noncommutative polynomial to have a vanishing cyclic gradient. Connections with free probability…
We study the relationship between the well-known Carleman's condition guaranteeing that a probability distribution is uniquely determined by its moments, and a recent easily checkable condition on the rate of growth of the moments. We use…
It is demonstrated that the statistical method of the famous Aspect - Bell experiment requires negative probability densities and negative probabilities from "the thing" researched, else that thing doesn't exist. The thing refers here to…
Using the existing classification of all alternatives to the measurement postulates of quantum theory we study the properties of bi-partite systems in these alternative theories. We prove that in all these theories the purification…
Square roots of probabilities appear in several contexts, which suggests that they are somehow more fundamental than probabilities. Square roots of probabilities appear in expressions of the Fisher-Rao Metric and the Hellinger-Bhattacharyya…
Symmetry of entangled states under a swap of outcomes ("envariance") implies their equiprobability, and leads to Born's rule. Here I show that the amplitude of a state given by a superposition of sequences of events that share same total…
This paper questions the generally accepted assumption that one can make a random choice that is independent of the rest of the universe. We give a general description of any setup that could be conceived to generate random numbers. Based…
We show that the Born's rule is incompatible with Lorentz symmetry of the Square Root Klein-Gordon equation (SRKG equation). It has been demonstrated that the Born rule must be modified in relativistic regime if one wishes to keep the SRKG…
Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the latter always result from an…
Let $L_n(k)$ denote the least common multiple of $k$ independent random integers uniformly chosen in $\{1,2,\ldots ,n\}$. In this note, using a purely probabilistic approach, we derive a criterion for the convergence in distribution as…
We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
This paper examines the concept of a combination rule for belief functions. It is shown that two fairly simple and apparently reasonable assumptions determine Dempster's rule, giving a new justification for it.
This work is devoted to the study of the probability of immunity, i.e. the effect occurs whether exposed or not. We derive necessary and sufficient conditions for non-immunity and $\epsilon$-bounded immunity, i.e. the probability of…