Related papers: On the consistency of the quantum-like representat…
We demonstrate the quantum probabilistic rule (which differ from classical Bayes' formula by the cosinus factor) can be obtained on purely classical basis as a consequence of the perturbation effect of preparation procedures. In any case…
The argument of environment-assisted invariance (known as envariance) implying Born's rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it…
In previous work of the authors, we investigated the Born and inverse Born series for a scalar wave equation with linear and nonlinear terms, the nonlinearity being cubic of Kerr type [8]. We reported conditions which guarantee convergence…
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…
In this treatise I introduce the time dependent Generalized Born's Rule for the probabilities of quantum events, including conditional and consecutive probabilities, as the unique fundamental time evolution equation of quantum theory. Then…
How can we take inspiration from a typical quantum algorithm to design heuristics for machine learning? A common blueprint, used from Deutsch-Josza to Shor's algorithm, is to place labeled information in superposition via an oracle,…
In this paper we establish the existence of the non-perturbative theory of quantum gravity known as quantum holonomy theory by showing that a Hilbert space representation of the QHD(M) algebra, which is an algebra generated by…
In this paper, we introduce elements of probabilistic model that is suitable for modeling of learning algorithms in biologically plausible artificial neural networks framework. Model is based on two of the main concepts in quantum physics -…
Quantum interference provides one of the most sensitive probes of quantum mechanics. While linear superposition fixes the positions and quadratic curvature of interference fringes, it remains unclear whether the probabilistic postulate…
Modern experiments using nanoscale devices come ever closer to bridging the divide between the quantum and classical realms, bringing experimental tests of objective collapse theories that propose alterations to Schr\"{o}dinger's equation…
In this paper we present a simple algorithm for representation of statistical data of any origin by complex probability amplitudes. Numerical simulation with Mathematica-6 is performed. The Bloch's sphere is used for visualization of…
We consider how the Born rule, a fundamental principle of quantum mechanics, can be tested for particles created on the shortest timescales ($\sim10^{-25}\,\mathrm{s}$) currently accessible at high-energy colliders. We focus on targeted…
The standard postulates of quantum theory can be divided into two groups: the first one characterizes the structure and dynamics of pure states, while the second one specifies the structure of measurements and the corresponding…
We study the following problem: Is it possible to explain the quantum interference of probabilities in the purely corpuscular model for elementary particles? We demonstrate that (by taking into account perturbation effects of measurement…
Quantum mechanics and gravitation are two pillars of modern physics. Despite their success in describing the physical world around us, they seem to be incompatible theories. There are suggestions that one of these theories must be…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
We show that the operational quantum formalism -- the Born rule, L\"uders state updating, quantum interference, non-Markovian effective dynamics, and Bell inequality violation at the Tsirelson bound $2\sqrt{2}$ -- arises within…
The asymptotic decision theory by Le Cam and Hajek has been given a lucid perspective by the Ibragimov-Hasminskii theory on convergence of the likelihood random field. Their scheme has been applied to stochastic processes by Kutoyants, and…
Born's rule, one of the cornerstones of quantum mechanics, relates detection probabilities to the modulus square of the wave function. Single-particle interference is accordingly limited to pairs of quantum paths and higher-order…
It is shown that the probability density satisfies a hyperbolic equation of motion with the unique characteristic that in its many-particle form it contains derivatives acting at spatially remote regions. Based on this feature we explore…