Related papers: Quantum Probability via the Method of Arbitrary Fu…
We deduce the Born rule. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics--a linear, not Hilbert', vector space--and empirical notion of the statistical length of a state. Its statistical nature…
We establish an operational rigidity result for a broad class of probability rules in infinite-dimensional settings, applicable under normality and steering assumptions. Starting from a topological generalization of generalized…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
We discuss the definition of quantum probability in the context of "timeless" general--relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum…
A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors are…
A model of correlated particles described by a generalized probability theory is suggested whose dynamics is subject to a non-linear version of Schr\"odinger equation. Such equations arise in many different contexts, most notably in the…
We propose a simple abstract formalisation of the act of observation, in which the system and the observer are assumed to be in a pure state and their interaction deterministically changes the states such that the outcome can be read from…
We compare and contrast two distinct approaches to understanding the Born rule in de Broglie-Bohm pilot-wave theory, one based on dynamical relaxation over time (advocated by this author and collaborators) and the other based on typicality…
Collapse of the wave function appears to violate the quantum superposition principle as well as deterministic evolution. Objective collapse models propose a dynamical explanation for this phenomenon, by making a stochastic non-unitary and…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
The partial trace is commonly introduced in quantum mechanics as an algebraic operation used to define reduced states of composite systems. However, the probabilistic origin of this operation goes systematically unnoticed in the literature.…
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…
In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the 'general tension-reduction' (GTR) model, able to describe general quantum-like measurements with an arbitrary number of…
We argue that the quantum probability law follows, in the large N limit, from the compatibility of quantum mechanics with classical-like properties of macroscopic objects. For a finite sample, we find that likely and unlikely measurement…
Dynamical quantum phase transitions (DQPTs) occur at times when a quantum state exhibits a nonanalytic change in its return probability. This can be viewed as the probability of collapsing the evolved state to the initial state by quantum…
Early in the development of quantum theory Bohr introduced what came to be called the Copenhagen interpretation. Specifically, the square of the absolute value of the wave function was to be used as a probability density. There followed…
Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this paper, we show that the complex nature of the quantum formalism can be derived directly from the…
This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…
We present a mathematical framework based on quantum interval-valued probability measures to study the effect of experimental imperfections and finite precision measurements on defining aspects of quantum mechanics such as contextuality and…