On Measures and Measurements: a Fibre Bundle approach to Contextuality

Cunha, Marcelo Terra

doi:10.48550/arxiv.1903.08819

Cited by 2 publications

(2 citation statements)

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“…An interesting prospect is to explore how the present framework may be employed to these ends, and to see whether the continuous-variable setting can open the door to new techniques that can be applied, or whether qualitatively new forms of contextual behaviour may be uncovered. A related direction to be developed is to understand how our treatment of contextuality can be further extended to continuous measurement spaces as proposed in [30].…”

Section: Discussionmentioning

confidence: 99%

“…We will still consider scenarios featuring only discrete sets of observables or measurements, as is typical in continuous-variable quantum computing. The possibility of considering contextuality in settings with continuous measurement spaces has also been evoked in [30]. We also note that several prior works have explicitly considered contextuality in continuous-variable systems [63,40,59,73,14,52,48].…”

Section: Introductionmentioning

confidence: 93%

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Continuous-Variable Nonlocality and Contextuality

Barbosa

Douce²,

Emeriau

et al. 2022

Commun. Math. Phys.

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Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It is increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been studied in discrete variable scenarios, where observables take values in discrete and usually finite sets. Practically, on the other hand, continuous-variable scenarios offer some of the most promising candidates for implementing quantum computations and informatic protocols. Here we set out a framework for treating contextuality in continuous-variable scenarios. It is shown that the Fine-Abramsky-Brandenburger theorem extends to this setting, an important consequence of which is that nonlocality can be viewed as a special case of contextuality, as in the discrete case. The contextual fraction, a quantifiable measure of contextuality that bears a precise relationship to Bell inequality violations and quantum advantages, can also be defined in this setting. It is shown to be a non-increasing monotone with respect to classical operations that include binning to discretise data. Finally, we consider how the contextual fraction can be formulated as an infinite linear program, and calculated with increasing accuracy using semi-definite programming approximations.

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Section: Discussionmentioning

confidence: 99%