Related papers: Quantiles Equivariance
We introduce the concept of quasi-inverse of quantum and classical channels, prove general properties of these inverses and determine them for a large class of channels acting in an arbitrary finite dimension. Therefore we extend the…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
The relations between Bell's inequality and quantum probability trees are explained against the background offered by the concept of a quantum probability tree built in others works. It is shown that f we use a concept of probability tree…
We describe a complete method for a precise study of gravitational interaction between two nearby quantum masses. Since the displacements of these masses are much smaller than the initial separation between their centers, the…
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.
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
A definition of quantum correlation is presented for an arbitrary bipartite quantum state based on the skew information. This definition not only inherits the good properties of skew information such as the contractivity and so on, but also…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…
Quantiles, such as the median or percentiles, provide concise and useful information about the distribution of a collection of items, drawn from a totally ordered universe. We study data structures, called quantile summaries, which keep…
A certain real number, depending on two neighbouring sides of a quadrilateral and the diagonal meeting these two sides at their common point, is shown to be invariant under affinity. As an application we demonstrate a nice formula for the…
We comment on the problem of energy translation invariance of probability distribution and present some observations. It is shown that a probability distribution can be invariant in the thermodynamic limit if there is no long term…
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…
Weak values are average quantities,therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as…
Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions.…
Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this,…
Gravity does not naturally fit well with canonical quantization. Affine quantization is an alternative procedure that is similar to canonical quantization but may offer a positive result when canonical quantization fails to offer a positive…
This paper extends quantile factor analysis to a probabilistic variant that incorporates regularization and computationally efficient variational approximations. We establish through synthetic and real data experiments that the proposed…
The statement that Maxwell's electrodynamics in vacuum is already covariant under Lorentz transformations is commonplace in the literature. We analyse the actual meaning of that statement and demonstrate that Maxwell's equations are…
A scenario is outlined for quantum measurement, assuming that self-sustaining classicality is the consequence of an attractive gravitational self-interaction acting on massive bodies, and randomness arises already in the classical domain. A…