Abstract
Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false and true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable configurations (also known as gadgets) deliver the strongest form of classical value indefiniteness. However, the choice of the respective configuration among all such collections, and thus the relation of its terminals, remains arbitrary and cannot be motivated by some superselection principle inherent to quantum or classical physics.
Highlights
Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false and true-implies-true, and nonseparability among the input and output terminals
One way to conceptualize the performance of quantized systems is in terms of boxes with input and output terminals as interfaces [14]
Once the terminal vertices are fixed, it is not too difficult to enumerate a quantum cloud that, interpreted classically, predicts and demands any kind of input-output behavior. This renders an element of arbitrariness in the interpretation of quantum clouds
Summary
The commonly used method for exploring nonclassicality is to consider configurations of type (i) with a quantum realization, upon which a classical interpretation, if it exists, is “enforced” in terms of uniform classical truth and falsity allocations of the associated propositions Such value assignments can be formalized by two-valued states s ∈ {0, 1} or (classical truth) value assignments, which are additive and add up to one whenever the propositions are exclusive and within a single context. (I) The “measures” or value assignments employed in so-called “contextuality inequalities” merely assume that every proposition is either true or false, regardless of the other propositions in that context, which are simultaneously measurable [32] This allows all possible 2d possibilities of value assignments in a d-dimensional context with d vertices, thereby vastly expanding the multitude of possible value assignments. Nonunitality in the sense of (u) discredits the classical predictions of quantum clouds even to a greater degree, probably only challenged by a complete absence of two-valued states
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