Continuous-variable nonlocality and contextuality

Barbosa, Rui Soares; Douce, Tom; Emeriau, Pierre-Emmanuel; Kashefi, Elham; Mansfield, Shane

doi:10.48550/arxiv.1905.08267

Cited by 7 publications

(12 citation statements)

References 49 publications

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“…Ref. [34] provides an analogous proof to Theorem 5 phrased in the continuousvariable extension [35] of the sheaf-theoretic framework for contextuality of Abramsky and Branderburger [26].…”

mentioning

confidence: 91%

Equivalence of contextuality and Wigner function negativity in continuous-variable quantum optics

Haferkamp¹,

Bermejo-Vega²

2021

Preprint

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“…Ref. [34] provides an analogous proof to Theorem 5 phrased in the continuousvariable extension [35] of the sheaf-theoretic framework for contextuality of Abramsky and Branderburger [26].…”

mentioning

confidence: 91%

Equivalence of contextuality and Wigner function negativity in continuous-variable quantum optics

Haferkamp¹,

Bermejo-Vega²

2021

Preprint

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“…with µ a measure on the set of ontic variables Λ. Let's also suppose that the theory satisfies the conditions for applying contextual fraction [24,37] 9 and, by simplicity, a finite number of outcomes for each measurement.…”

Section: Applications a Relation With Contextual Fractionmentioning

confidence: 99%

“…Non-disturbance is defined in the intersection of contexts: if the valuation of an intersection (when one defines it) ξ (C ∩ C ′ ) is independent of C and C ′ for all pairs of contexts, then M is said to be non-disturbing. It is related to parameter-independence[23,24] 2. Outcome-determinism is defined in the valuation: the outcomes defined on the contexts where the distribution is defined can be explained in a deterministic way.…”

mentioning

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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“…The interested reader can consult works such as [169] that relate Wigner negativity to the more general concept of quantum contextuality. However, the topic of contextuality in CV systems is still a matter of scientific debate [170].…”

Section: Non-gaussianity and Bell Inequalitiesmentioning

confidence: 99%

Non-Gaussian Quantum States and Where to Find Them

Walschaers

2021

Preprint

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Gaussian states have played on important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description. Nevertheless, many proposed quantum technologies require us to go beyond the realm of Gaussian states and introduce non-Gaussian elements. In this Tutorial, we provide a roadmap for the physics of non-Gaussian quantum states. We introduce the phase-space representations as a framework to describe the different properties of quantum states in continuous-variable systems. We then use this framework in various ways to introduce extra structure in the state space. We explain how non-Gaussian states can be characterised not only through the negative values of their Wigner function, but also via other properties such as quantum non-Gaussianity and the related stellar rank. For multimode systems, we are naturally confronted with the question of how non-Gaussian properties behave with respect to quantum correlations. To answer this question, we first show how non-Gaussian states can be created by performing measurements on a subset of modes in a Gaussian state. Then, we highlight that these measured modes must be correlated via specific quantum correlations to the remainder of the system to create quantum non-Gaussian or Wigner-negative states. On the other hand, non-Gaussian operations are also shown to enhance or even create quantum correlations. Finally, we will demonstrate that Wigner negativity is a requirement to violate Bell inequalities and to achieve a quantum computational advantage. At the end of the Tutorial, we also provide an overview of several experimental realisations of non-Gaussian quantum states in quantum optics and beyond.

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Continuous-variable nonlocality and contextuality

Cited by 7 publications

References 49 publications

Equivalence of contextuality and Wigner function negativity in continuous-variable quantum optics

Equivalence of contextuality and Wigner function negativity in continuous-variable quantum optics

Differential Geometry of Contextuality

Non-Gaussian Quantum States and Where to Find Them

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