Related papers: Born Rule and Noncontextual Probability

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…

A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well…

The Born rule is part of the collapse axiom in the standard version of quantum theory, as presented by standard textbooks on the subject. We show here that its signature quadratic dependence follows from a single additional physical…

Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be…

Despite the tremendous empirical success of quantum theory there is still widespread disagreement about what it can tell us about the nature of the world. A central question is whether the theory is about our knowledge of reality, or a…

The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual…

Gleason's theorem is a fundamental 60 year old result in the foundations of quantum mechanix, setting up and laying out the surprisingly minimal assumptions required to deduce the existence of quantum density matrices and the Born rule. Now…

Gleason's theorem [A. Gleason, J. Math. Mech., \textbf{6}, 885 (1957)] is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it…

Quantum decision theory is introduced here, and new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, next on arguments for the Born rule, that is,…

We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…

Zurek has derived the quantum probabilities for Schmidt basis states of bipartite quantum systems in pure joint states, from the assumption that they should be not be affected by one party's action if the action can be undone by the other…

It is argued that there is no evidence for causality as a metaphysical relation in quantum phenomena. The assumption that there are no causal laws, but only probabilities for physical processes constrained by symmetries, leads naturally to…

Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…

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…

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…

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…

The Born rule provides a fundamental connection between theory and observation in quantum mechanics, yet its origin remains a mystery. We consider this problem within the context of quantum optics using only classical physics and the…

In the context of generalized measurement theory, the Gleason-Busch theorem assures the unique form of the associated probability function. Recently, in Flatt et al. Phys. Rev. A 96, 062125 (2017), the case of subsequent measurements has…

In the last five years of his life Itamar Pitowsky developed the idea that the formal structure of quantum theory should be thought of as a Bayesian probability theory adapted to the empirical situation that Nature's events just so happen…

We raise the issue whether conventional quantum mechanics, which is not a hidden variable theory in the usual Jauch-Piron's sense, might nevertheless be a hidden variable theory in the sense recently conjectured by G. 't Hooft in his…