Related papers: The Born rule from a consistency requirement on hi…
Let $V=\mathbb{C}^N$, and $H$ (an observable) a Hermitian linear operator on $V$. Let $v_1,..., v_n$ be an orthonormal basis for $V$. Let $\mathcal{M}$ be a measurement apparatus prepared to measure a state of an observed system and…
We first review and critically examine some basic concepts and ambiguities related to quantum mechanics and quantum measurement to understand the success and shortcomings of current theories. We also touch on ideas regarding expression of…
We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a…
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…
Details of the contents and the formulations of the Born rule changed considerably from its inception by Born in 1926 to the present day. This paper traces the early history of the Born rule 100 years ago, its generalization (essential for…
The goal of this paper is to apply the collection of mathematical tools known as the "method of arbitrary functions" to analyze how probability arises from quantum dynamics. We argue that in a toy model of quantum measurement the Born rule…
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…
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 -…
I argue that various derivations of the Born probability rule within strictly unitary quantum mechanics implicitly use anthropic constraints on the properties of the probabilities, but without proposing an ensemble from which those…
According to the subjective Bayesian interpretation of quantum theory (QBism), quantum mechanics is a tool that an agent would be wise to use when making bets about natural phenomena. In particular, the Born rule is understood to be a…
We present a generic model of (non-destructive) quantum measurement. Being formulated within reversible quantum mechanics, the model illustrates a mechanism of a measurement process --- a transition of the measured system to an eigenstate…
A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers…
The paper discuss the structure of quantum mechanics and uniqueness of its postulates. The Born rule for quantum probabilities is fixed by requirement of nonexistence of quantum telepathy. Von Neumann projection postulate describes the…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a…
We present a very general geometrico-dynamical description of physical or more abstract entities, called the 'general tension-reduction' (GTR) model, where not only states, but also measurement-interactions can be represented, and the…
A realist description of our universe requires a twofold concept of locality. On one hand, there are the strictly Einstein-local interactions which generate the time evolution. On the other hand, the quantum state space calls for a…
The Born rule is at the foundation of quantum mechanics and transforms our classical way of understanding probabilities by predicting that interference occurs between pairs of independent paths of a single object. One consequence of the…
The quantum formalism can be completed by assuming that a density operator can also represent a pure state. An 'extended Bloch representation' (EBR) then results, in which not only states, but also the measurement-interactions can be…
A principle of information conservation is shown in abstract terms to rule out probabilistic physical laws, necessitating the existence of state trajectories. It furthermore provides a geometric-thermodynamic mechanism for the appearance of…