Related papers: Quantum conditional probabilities
As it is known, Gleason's theorem is not applicable for a two-dimensional Hilbert space since in this situation Gleason's axioms are not strong enough to imply Born's rule thus leaving room for a dispersion-free probability measure i.e.,…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
A basic postulate of modern compositional approaches to generalised physical theories is the generalised Born rule, in which probabilities are postulated to be computable from the composition of states and effects. In this paper we consider…
Born's rule is the recipe for calculating probabilities from quantum mechanical amplitudes. There is no generally accepted derivation of Born's rule from first principles. In this paper, it is motivated from assumptions that link the…
We remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative -- either nonlocality or ``death of reality'' (under the assumption the quantum mechanics is incomplete). Violation…
Quantum theory does not provide a unique definition for the joint probability of two non-commuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were…
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…
Page has recently argued that the Born rule does not suffice for computing all probabilities in quantum cosmology. He further asserts that the Born rule's failure gives rise to the cosmological measure problem. Here I contend that Page's…
We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures (POVMs), as opposed to the restricted class of orthogonal projection-valued measures used in the original…
The celebrating theorem of A. Fine implies that the CHSH inequality is violated if and only if the joint probability distribution for the quadruples of observables involved the EPR-Bohm-Bell experiment does not exist, i.e., it is impossible…
We establish connections between the requirement of measurability of a probability space and the principle of complimentarity in quantum mechanics. It is shown that measurability of a probability space implies the dependence of results of…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that…
The auxiliary rules of quantum mechanics have always included the Born rule that connects probability with square modulus. This need not be the case, for it is possible to introduce probability into the theory through probability current…
Mainstream interpretations of quantum theory maintain that violations of the Bell inequalities deny at least either realism or Einstein locality. Here we investigate the premises of the Bell-type inequalities by returning to earlier…
In this paper we continue to study so called ``inverse Born's rule problem'': to construct representation of probabilistic data of any origin by a complex probability amplitude which matches Born's rule. The corresponding algorithm --…