Ontological Models, Preparation Contextuality and Nonlocality

Banik, Manik; Bhattacharya, Some Sankar; Choudhary, Sujit K.; Mukherjee, Amit; Roy, Arup

doi:10.1007/s10701-014-9839-4

Cited by 20 publications

(29 citation statements)

References 31 publications

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“…Furthermore, we show that restricted preparation contextuality of quantum theory leads to its limited nonlocal behavior as depicted in the Cirel'son bound. Therefore, our result brings the qualitative connection between preparation contextuality and nonlocality explored in [12][13][14] to a quantitative footing.…”

Section: Arxiv:150605174v2 [Quant-ph] 12 Sep 2015mentioning

confidence: 57%

“…It was then shown that mixed preparations (density matrices) in quantum theory exhibit preparation contextuality [9,12]. Interestingly, invoking another non-classical concept called steering [10,11] along with this new idea of preparation contextuality one can establish nonlocality of QM without using any Bell type inequalities; it has been shown that nonlocality of some hidden variable models, underlying QM, directly follows from the steerability of bipartite pure entangled states and the preparation contextuality of mixed states [12][13][14].The traditional definition of contexuality address to only the contexts of projective measurements, which has been studied in much depth [15,16]. However, generalized notion of contextuality developed by Spekkens define three different types of contexts: measurement (generalized), preparation, and transformation contexts [9].…”

mentioning

confidence: 99%

“…However, generalized notion of contextuality developed by Spekkens define three different types of contexts: measurement (generalized), preparation, and transformation contexts [9]. Interest in studying contextuality in this general framework is relatively new and growing [12][13][14][17][18][19][20]. This generalized approach has lead to designing more robust experimental tests of contextuality [18][19][20]; these recent results are very promising given that previously requirements for testing contextuality in experiments has been a topic of much controversy ( for a more discussion see the ref.…”

mentioning

confidence: 99%

“…However, recently the idea of KS contextuality has been generalized, by Spekkens [9], for arbitrary operational theories rather than just quantum theory and for arbitrary experimental procedures rather than just sharp measurements. It was then shown that mixed preparations (density matrices) in quantum theory exhibit preparation contextuality [9,12]. Interestingly, invoking another non-classical concept called steering [10,11] along with this new idea of preparation contextuality one can establish nonlocality of QM without using any Bell type inequalities; it has been shown that nonlocality of some hidden variable models, underlying QM, directly follows from the steerability of bipartite pure entangled states and the preparation contextuality of mixed states [12][13][14].…”

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confidence: 99%

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Limited preparation contextuality in quantum theory and its relation to the Cirel'son bound

et al. 2015

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Kochen-Specker (KS) theorem lies at the heart of the foundations of quantum mechanics. It establishes impossibility of explaining predictions of quantum theory by any noncontextual ontological model. Spekkens generalized the notion of KS contextuality in [Phys. Rev. A 71, 052108 (2005)] for arbitrary experimental procedures (preparation, measurement, and transformation procedure). Interestingly, later on it was shown that preparation contextuality powers parity-oblivious multiplexing [Phys. Rev. Lett. 102, 010401 (2009)], a two party information theoretic game. Thus, using resources of a given operational theory, the maximum success probability achievable in such a game suffices as a bona-fide measure of preparation contextuality for the underlying theory. In this work we show that preparation contextuality in quantum theory is more restricted compared to a general operational theory known as box world. Moreover, we find that this limitation of quantum theory implies the quantitative bound on quantum nonlocality as depicted by the Cirel'son bound.Quantum mechanics (QM) departs fundamentally from the well known local-realistic world view of classical physics. This stark contrast of quantum theory with classical physics was illuminated by J. S. Bell [1]. Since the Bell's seminal work, nonlocality remains at the center of quantum foundational research [2,3]. More recently quantum nonlocality has been also established as a key resource for device independent information technology [3,4]. Quantum nonlocality does not contradict the relativistic causality principle, however, QM is not the only possible theory that exhibits nonlocality along with satisfying the no-signaling principle; there can be nonquantum no-signaling correlations exhibiting nonlocality. One extreme example of such a correlation (more nonlocal than QM) was first constructed by Popescu and Rohrlich (PR) [5]. Whereas PR correlation violates the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) [1,6] inequality by algebraic maximum, the optimal Bell-CHSH violation in quantum theory is restricted by the Cirel'son bound [7]. In this work, we show that Cirel'son limit on nonlocal behavior of quantum theory can be explained from its another very interesting feature, namely restricted preparation contextuality.Nearly at the same time of Bell's result, Kochen and Specker proved another important no-go theorem showing that predictions of sharp (projective) measurements in QM can not be reproduced by any non-contextual ontological model [8]. Unlike Bell-nonlocality, structure of QM is implicit in the definition of KS contextuality. However, recently the idea of KS contextuality has been generalized, by Spekkens [9], for arbitrary operational theories rather than just quantum theory and for arbitrary experimental procedures rather than just sharp measurements. It was then shown that mixed preparations (density matrices) in quantum theory exhibit preparation contextuality [9,12]. Interestingly, invoking another non-classical concept called steering [10,11] along with ...

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Section: Arxiv:150605174v2 [Quant-ph] 12 Sep 2015mentioning

confidence: 57%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Limited preparation contextuality in quantum theory and its relation to the Cirel'son bound

et al. 2015

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“…It is also known that preparation noncontextual models underlying quantum theory must be maximally epistemic, and these in turn must be Kochen-Specker noncontextual [15]. Moreover, the concept of preparation contextuality has been used to demonstrate nonlocality of some ψ-epistemic models without any use of Bell's inequality [12,15]. Along with its foundational implications, preparation contextuality has an important ramification in certain information theoretic task.…”

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confidence: 99%

Parity oblivious d-level random access codes and class of noncontextuality inequalities

Ambainis

Banik

Chaturvedi

et al. 2019

Quantum Inf Process

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One of the fundamental results in quantum foundations is the Kochen-Specker no-go theorem. For the quantum theory, the no-go theorem excludes the possibility of a class of hidden variable models where value attribution is context independent. Recently, the notion of contextuality has been generalized for different operational procedures and it has been shown that preparation contextuality of mixed quantum states can be a useful resource in an information-processing task called parityoblivious multiplexing. Here, we introduce a new class of information processing tasks, namely d-level parity oblivious random access codes and obtain bounds on the success probabilities of performing such tasks in any preparation noncontextual theory. These bounds constitute noncontextuality inequalities for any value of d. For d = 3, using a set of mutually asymmetric biased bases we show that the corresponding noncontextual bound is violated by quantum theory. We also show quantum violation of the inequalities for some other higher values of d. This reveals operational usefulness of preparation contextuality of higher level quantum systems.

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Measurement incompatibility and Schrödinger-Einstein-Podolsky-Rosen steering in a class of probabilistic theories

Banik

2015

Journal of Mathematical Physics

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Steering is one of the most counter intuitive non classical features of bipartite quantum system, first noticed by Schrödinger at the early days of quantum theory. On the other hand measurement incompatibility is another non classical feature of quantum theory, initially pointed out by N. 160403 (2014)] have investigated the relation between these two distinct non classical features. They have shown that a set of measurements is not jointly measurable (i.e. incompatible) if and only if they can be used for demonstrating Schrödinger-Einstein-Podolsky-Rosen steering. The concept of steering has been generalized for more general abstract tensor product theories rather than just Hilbert space quantum mechanics. In this article we discuss that the notion of measurement incompatibility can be extended for general probability theories. Further we show that the connection between steering and measurement incompatibility holds in a border class of tensor product theories rather than just quantum theory.

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Ontological Models, Preparation Contextuality and Nonlocality

Cited by 20 publications

References 31 publications

Limited preparation contextuality in quantum theory and its relation to the Cirel'son bound

Limited preparation contextuality in quantum theory and its relation to the Cirel'son bound

Parity oblivious d-level random access codes and class of noncontextuality inequalities

Measurement incompatibility and Schrödinger-Einstein-Podolsky-Rosen steering in a class of probabilistic theories

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