Related papers: The Born rule from a consistency requirement on hi…
We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold -- these…
The preferred-basis problem and the definite-outcome aspect of the measurement problem persist even when the detector is modeled unitarily. Experimental data are represented in a Boolean event algebra of mutually exclusive records, while…
We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and…
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…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then…
Spontaneous collapse models use non-linear stochastic modifications of the Schroedinger equation to suppress superpositions of eigenstates of the measured observable and drive the state to an eigenstate. It was recently demonstrated that…
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…
Nelson's stochastic mechanics may be understood as a stochastic underpinning, or reconstruction, of nonrelativistic quantum mechanics, once the diffusion scale is fixed by $\hbar$ and the admissible states are restricted by the usual…
Quantum dynamics of the collective mode and individual particles on a ring is studied as the simplest model of projective quantum measurement. In this model, the collective mode measures an individual single quantum system. The heart of the…
We first prove that ontological models of the quantum state which are capable of reproducing the Born probability rule and fall in the class of $\psi$-epistemic models are inconsistent with the Sch{\"o}dinger time evolution. We then model…
Probabilities enter quantum mechanics via Born's rule, the uniqueness of which was proven by Gleason. Busch subsequently relaxed the assumptions of this proof, expanding its domain of applicability in the process. Extending this work to…
As a fundamental postulate of quantum mechanics, Born's rule assigns probabilities to the measurement outcomes of quantum systems and excludes multi-order quantum interference. Here we report an experiment on a single spin in diamond to…
A concise review of the derivation of the Born rule and Schr\"odinger equation from first principles is provided. The starting point is a formalization of fundamental notions of measurement and composition, leading to a general framework…
The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In $\psi$-ontic quantum theories, reality is directly represented by the wavefunction. We show that…
Classical approaches often treat interaction as engineered product terms or as emergent patterns in flexible models, offering little control over how synergy or antagonism arises. We take a quantum-inspired view: following the Born rule…
Quantum coherence and distributed correlations among subparties are often considered as separate, although operationally linked to each other, properties of a quantum state. Here, we propose a measure able to quantify the contributions…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
In Everett's many worlds interpretation, quantum measurements are considered to be decoherence events. If so, then inexact decoherence may allow large worlds to mangle the memory of observers in small worlds, creating a cutoff in observable…
Nelson's stochastic quantum mechanics provides an ideal arena to test how the Born rule is established from an initial probability distribution that is not identical to the square modulus of the wave function. Here, we investigate…