Contextuality without incompatibility

Selby, John H.; Schmid, David; Wolfe, Elie; Sainz, Ana Belén; Kunjwal, Ravi; Spekkens, Robert W.

doi:10.48550/arxiv.2106.09045

Cited by 4 publications

(9 citation statements)

References 38 publications

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“…This result can be viewed as the generalisation of the result of our companion paper, Ref. [8], to arbitrary proofs of contextuality in arbitrary GPTs.…”

Section: Introductionsupporting

confidence: 64%

“…Our first example of cone-equivalent accessible GPT fragments arises from a process that we call flag-convexification [8,9]. Suppose that we have a prepare and measure scenario described by a multisource and multimeter as in Eq.…”

Section: A Example 1: Flag-convexified Scenariosmentioning

confidence: 99%

“…(Flag-convexification, introduced in Refs. [8,9], is a process by which measurement settings are turned into measurement outcomes.) Moreover, as discussed in detail in Sec.…”

Section: Introductionmentioning

confidence: 99%

“…For any scenario with multiple measurements, one can apply the flag-convexification procedure of Ref. [8] to turn the measurement settings into measurement outcomes, so that the resulting scenario has only a single measurement. As we will prove, this flag-convexified scenario is cone-equivalent to the original scenario, and hence either both are classically explainable, or both are not.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

Selby¹,

Schmid²,

Wolfe³

et al. 2021

Preprint

Self Cite

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The formalism of generalized probabilistic theories (GPTs) was originally developed as a way to characterize the landscape of conceivable physical theories. Thus, the GPT describing a given physical theory necessarily includes all physically possible processes. We here consider the question of how to provide a GPT-like characterization of a particular experimental setup within a given physical theory. We show that the resulting characterization is not generally a GPT in and of itself-rather, it is described by a more general mathematical object that we introduce and term an accessible GPT fragment. We then introduce an equivalence relation, termed cone equivalence, between accessible GPT fragments (and, as a special case, between standard GPTs). We give a number of examples of experimental scenarios that are best described using accessible GPT fragments, and where moreover cone-equivalence arises naturally. We then prove that an accessible GPT fragment admits of a classical explanation if and only if every other fragment that is cone-equivalent to it also admits of a classical explanation. Finally, we leverage this result to prove several fundamental results regarding the experimental requirements for witnessing the failure of generalized noncontextuality. In particular, we prove that neither incompatibility among measurements nor the assumption of freedom of choice is necessary for witnessing failures of generalized noncontextuality, and, moreover, that such failures can be witnessed even using arbitrarily inefficient detectors.

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“…This result can be viewed as the generalisation of the result of our companion paper, Ref. [8], to arbitrary proofs of contextuality in arbitrary GPTs.…”

Section: Introductionsupporting

confidence: 64%

Section: A Example 1: Flag-convexified Scenariosmentioning

confidence: 99%

“…(Flag-convexification, introduced in Refs. [8,9], is a process by which measurement settings are turned into measurement outcomes.) Moreover, as discussed in detail in Sec.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

Selby¹,

Schmid²,

Wolfe³

et al. 2021

Preprint

Self Cite

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show abstract

“…The notion of generalized contextuality [27], dealing with preparations, transformations, and unsharp measurements (this one equivalent to effect algebras), is a way to inquire about the classicality of a system through operational equivalences. Operational equivalence on the states, the effects, and the transformations can be written as linear conditions [28] ∑ s a (α)…”

Section: Generalized Contextualitymentioning

confidence: 99%

Differential Geometry of Contextuality

Montanhano¹

2022

Preprint

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Contextuality has been related for a long time as a topological phenomenon. In this work, such a relationship is exposed in the more general framework of generalized contextuality. The main idea is to identify states, effects, and transformations as vectors living in a tangent space, and the non-contextual conditions as discrete closed paths implying null vertical phases. Two equivalent interpretations hold. The geometrical or realistic view, where flat space is imposed, implies that the contextual behavior becomes equivalent to the curvature (nontrivial holonomy) of the probabilistic functions, in analogy with the electromagnetic tensor; as a modification of the valuation function, it can be used to connect contextuality with interference, non-commutativity, and signed measures. The topological or anti-realistic view, where the valuation functions must be preserved, implies that the contextual behavior can be translated as topological failures (non-trivial monodromy); it can be used to connect contextuality with non-embeddability and a generalized Voroby'ev theorem. Both views can be related to contextual fraction, and the disturbance in ontic models can be presented as non-trivial transition maps.

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Incompatibility in restricted operational theories: connecting contextuality and steering

Plávala

2022

J. Phys. A: Math. Theor.

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We investigate the connection between steering and contextuality in general probabilistic theories. We show that for a class of bipartite states the steerability of the state by a given set of measurements is equivalent to non-existence of preparation noncontextual hidden variable model for certain restricted theory constructed from the given state and measurements. The connection between steering and contextuality is provided by the concept of incompatibility in restricted theory, which we also investigate.

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Contextuality without incompatibility

Cited by 4 publications

References 38 publications

Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

Differential Geometry of Contextuality

Incompatibility in restricted operational theories: connecting contextuality and steering

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