Quantum prescriptions are more ontologically distinct than they are operationally distinguishable

Chaturvedi, Anubhav; Saha, Debashis

doi:10.22331/q-2020-10-21-345

Cited by 12 publications

(14 citation statements)

References 39 publications

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“…[Pus18] and generally in Ref. [CS20]. Finally, Observation 7 is implied by the connection between compatibility scenarios and Kochen-Specker contextuality scenarios [ATC18] (which can further be translated to generalised contextuality scenarios [KS18]), together with the fact that certain compatibility scenarios necessitate unsharp measurements [KHF14].…”

Section: Quantum Contextual Set and Subsetsmentioning

confidence: 90%

“…In analogy with quantum non-locality [BCP + 14], quantum theory surpasses these noncontextual limitations, but not necessarily to the maximum mathematically possible extent [BBM + 15]. Bounding this violation provides foundational insights, such as establishing how distinct operationally indistinguishable entities must be in order to explain quantum predictions [CS20,Mar20], and finds technological applications in capping quantum advantage. Despite this motivation, the nature and the extent of available quantum contextuality remains largely uncharacterised.…”

Section: Introductionmentioning

confidence: 99%

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Characterising and bounding the set of quantum behaviours in contextuality scenarios

Chaturvedi

Farkas

Wright

2021

Quantum

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The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios, including contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations, we demonstrate monogamy of preparation contextuality in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.

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Section: Quantum Contextual Set and Subsetsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Characterising and bounding the set of quantum behaviours in contextuality scenarios

Chaturvedi

Farkas

Wright

2021

Quantum

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“…However, even after almost a century since its conception, there is no consensus about the precise sense in which the structure of reality that quantum theory posits conflicts with classical worldviews. Addressing such questions necessitates formal notions of classicality, and the realist (ontological) framework provides a vital ground for such notions [1][2][3][4].…”

mentioning

confidence: 99%

“…Generalised noncontextuality attributes identical realist counterparts to operationally equivalent physical entities, and the operational indistinguishability of these entities forms the prerequisite of experimental tests of noncontextuality [3]. The recently introduced notion of classicality, bounded ontological distinctness (BOD) explains the distinguishability of operational physical entities by the distinctness of their realist counterparts, and p-distinguishability of the physical entities forms a prerequisite of the experimental tests of BOD [4]. 1 Bell's local-causality entails two distinct realist assumptions.…”

mentioning

confidence: 99%

“…On the other hand, the realist notions of classicality yield empirically falsifiable operational consequences, typically in the form of statistical inequalities. The quantum violation of these inequalities not only highlights the necessity of realist fine-tuning, discarding a large class of realist explanations, but also powers quantum advantage in a plethora of computational, communication and information processing tasks [4,[7][8][9]. Therefore, empirically falsifiable phenomena feature as the operational prerequisites, as well as the operational consequences of the realist notions of classicality.…”

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confidence: 99%

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Quantum description of reality is empirically incomplete

Chaturvedi¹,

Pawłowski²,

Saha³

2021

Preprint

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An Operational Notion of Classicality Based on Physical Principles

Sarkar

2023

Found Phys

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One of the basic observations of the classical world is that physical entities are real and can be distinguished from each other. However, within quantum theory, the idea of physical realism is not well established. A framework to analyse how observations in experiments can be described using some physical states of reality was recently developed, known as ontological models framework. Different principles when imposed on the ontological level give rise to different theories, the validity of which can be tested based on the statistics generated by these theories. Using the ontological models framework, we formulate a novel notion of classicality termed ontic-distinguishability, which is based upon the physical principles that in classical theories extremal states are physical states of reality and every sharp measurement observes the state of the system perfectly. We construct a communication task in which the success probability is bounded from above for ontological models satisfying the notion of ontic-distinguishability. Contrary to previous notions of classicality which either required systems of dimension strictly greater than two or atleast three preparations, a violation of ontic-distinguishability can be observed using just a pair of qubits and a pair of incompatible measurements. We further show that violation of previously known notions of classicality such as preparation non-contextuality and Bell’s local causality is a violation of ontic-distinguishability.

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Quantum prescriptions are more ontologically distinct than they are operationally distinguishable

Cited by 12 publications

References 39 publications

Characterising and bounding the set of quantum behaviours in contextuality scenarios

Characterising and bounding the set of quantum behaviours in contextuality scenarios

Quantum description of reality is empirically incomplete

An Operational Notion of Classicality Based on Physical Principles

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