Abstract
Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability (vimeo.com/52923835). To date, Specker's principle seemed incapable of singling out quantum theory from the space of all general probabilistic theories. In particular, its well-known consequence for experimental statistics, the principle of consistent exclusivity, does not rule out the set of correlations known as almost quantum, which is strictly larger than the set of quantum correlations. Here we show that, contrary to the popular belief, Specker's principle cannot be satisfied in any theory that yields almost quantum correlations.
Highlights
The advent of quantum theory was accompanied by many conceptual controversies over the failure of intuitions from classical physics, e.g. the existence of wave-particle duality, the fundamental indeterminism apparent from the Born rule, and the nonseparability epitomized by entanglement, as pointed out by Einstein, Podolsky and Rosen [1, 2]
Since projective measurements in quantum theory satisfy the principle of pairwise sufficiency, the set Q(H) for an events-based hypergraph H obtained from an (n, 2) symmetric marginal scenario coincides with C(H)
In the following we argue that (i) any definition of sharp measurements in a theory that yields almost quantum correlations must violate Specker’s principle, and (ii) any notion of sharpness in an almost quantum theory must deviate from the candidates proposed so far [31, 32]
Summary
The advent of quantum theory was accompanied by many conceptual controversies over the failure of intuitions from classical physics, e.g. the existence of wave-particle duality, the fundamental indeterminism apparent from the Born rule, and the nonseparability epitomized by entanglement, as pointed out by Einstein, Podolsky and Rosen [1, 2]. Statistical aspects of quantum theory come into play when exploring phenomena such as Bell nonlocality [4] and Kochen-Specker (KS) contextuality [5] These cannot be explained by a classical model of the world, they arise naturally within quantum theory. We explore the structural aspects of a hypothetical almost quantum theory by investigating its statistical aspects—almost quantum correlations To this end, we use the connections between two frameworks for describing contextuality scenarios: in terms of compatible measurements [7], and in terms of operational equivalences among measurement events [8]. These include a family of sufficiency properties which we define therein.
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