828 research outputs found
Embedding Quantum into Classical: Contextualization vs Conditionalization
We compare two approaches to embedding joint distributions of random
variables recorded under different conditions (such as spins of entangled
particles for different settings) into the framework of classical,
Kolmogorovian probability theory. In the contextualization approach each random
variable is "automatically" labeled by all conditions under which it is
recorded, and the random variables across a set of mutually exclusive
conditions are probabilistically coupled (imposed a joint distribution upon).
Analysis of all possible probabilistic couplings for a given set of random
variables allows one to characterize various relations between their separate
distributions (such as Bell-type inequalities or quantum-mechanical
constraints). In the conditionalization approach one considers the conditions
under which the random variables are recorded as if they were values of another
random variable, so that the observed distributions are interpreted as
conditional ones. This approach is uninformative with respect to relations
between the distributions observed under different conditions, because any set
of such distributions is compatible with any distribution assigned to the
conditions.Comment: PLoS One 9(3): e92818 (2014
Conversations on Contextuality
In the form of a dialogue (imitating in style Lakatos's Proof and
Refutation), this chapter presents and explains the main points of the approach
to contextuality dubbed Contextuality-by-Default.Comment: Opening chapter (pp. 1-22) in "Contextuality from Quantum Physics to
Psychology," edited by E. Dzhafarov, S. Jordan, R. Zhang, V. Cervantes. New
Jersey: World Scientific Press, 201
Contextuality in Three Types of Quantum-Mechanical Systems
We present a formal theory of contextuality for a set of random variables
grouped into different subsets (contexts) corresponding to different, mutually
incompatible conditions. Within each context the random variables are jointly
distributed, but across different contexts they are stochastically unrelated.
The theory of contextuality is based on the analysis of the extent to which
some of these random variables can be viewed as preserving their identity
across different contexts when one considers all possible joint distributions
imposed on the entire set of the random variables. We illustrate the theory on
three systems of traditional interest in quantum physics (and also in
non-physical, e.g., behavioral studies). These are systems of the
Klyachko-Can-Binicioglu-Shumovsky-type, Einstein-Podolsky-Rosen-Bell-type, and
Suppes-Zanotti-Leggett-Garg-type. Listed in this order, each of them is
formally a special case of the previous one. For each of them we derive
necessary and sufficient conditions for contextuality while allowing for
experimental errors and contextual biases or signaling. Based on the same
principles that underly these derivations we also propose a measure for the
degree of contextuality and compute it for the three systems in question.Comment: Foundations of Physics 7, 762-78
- …