Related papers: Characterizing common cause closedness of quantum …
It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains…
States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally…
If \{A(V)\} is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V_1 and V_2 are spacelike separated spacetime regions, then the system (A(V_1),A(V_2),\phi) is said to satisfy…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional…
This pedagogical article solves an interesting problem in quantum measure theory. Although a quantum measure $\mu$ is a generalization of an ordinary probability measure, $\mu$ need not satisfy the usual additivity condition. Instead, $\mu$…
In classic cases, Reichenbach's principle implies that discriminating between common causes and causality is unprincipled since the discriminative results essentially depend on the selection of possible conditional variables. For some…
In the paper it will be shown that Reichenbach's Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A and B supported in…
The principle of the common cause claims that if an improbable coincidence has occurred, there must exist a common cause. This is generally taken to mean that positive correlations between non-causally related events should disappear when…
It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections in local von Neumann algebras $\cA(V_1),\cA(V_2)$ associated with spacelike separated spacetime regions $V_1,V_2$…
Reichenbach defined a common cause which explains a correlation between two events if either one does not cause the other. Its intuitive idea is that the statistical ensemble can be divided into two disjoint parts so that the correlation…
Bell's 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbach's Principle of Common Cause. Despite being a hallmark of scientific thought, dropping the principle has been…
In a recent paper it was shown that all the Hilbert space formulas for quantum probabilities can be realized as functions of geometric properties of the associated projective space, but those functions were expressed using the structures of…
Reichenbach's Common Cause Principle claims that if there is correlation between two events and none of them is directly causally influenced by the other, then there must exist a third event that can, as a common cause, account for the…
Projection factors describe the contraction of Lebesgue measures in orthogonal projections between subspaces of a real or complex inner product space. They are connected to Grassmann's exterior algebra and the Grassmann angle between…
We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability vectors in terms of…
Quantum-mechanical observables for spatial and spacetime localization are considered from a lattice-theoretic perspective. It is shown that when replacing the lattice of all complex orthogonal projections underlying the Born rule by the…
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…
We introduce the coordination principle, which states that perfect coordination, in the form of agreement on a uniformly random output, among N parties is possible only if they share a common cause. This principle is purely causal and can…
Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum…