Maximally Epistemic Interpretations of the Quantum State and Contextuality

Leifer, Matthew; Maroney, O. J. E.

doi:10.1103/physrevlett.110.120401

Cited by 86 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].…”

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confidence: 99%

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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.…”

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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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“…In Refs. [12,13], the question is raised whether ψ-epistemic models can reproduce quantum predictions given an assumption about the extent to which the epistemic states overlap.Refs. [12,13] are the most direct precursors to this work, since here we are also concerned with the extent to which the distributions µ ψ and µ φ can overlap in models which recover the predictions of quantum theory.…”

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Noψ-Epistemic Model Can Fully Explain the Indistinguishability of Quantum States

et al. 2014

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According to a recent no-go theorem (M. Pusey, J. Barrett and T. Rudolph, Nature Physics 8 475 (2012)), models in which quantum states correspond to probability distributions over the values of some underlying physical variables must have the following feature: the distributions corresponding to distinct quantum states do not overlap. This is significant because if the distributions do not overlap, then the quantum state itself is encoded by the physical variables. In such a model, it cannot coherently be maintained that the quantum state merely encodes information about underlying physical variables. The theorem, however, considers only models in which the physical variables corresponding to independently prepared systems are independent. This work considers models that are defined for a single quantum system of dimension d, such that the independence condition does not arise. We prove a result in a similar spirit to the original no-go theorem, in the form of an upper bound on the extent to which the probability distributions can overlap, consistently with reproducing quantum predictions. In particular, models in which the quantum overlap between pure states is equal to the classical overlap between the corresponding probability distributions cannot reproduce the quantum predictions in any dimension d ≥ 3. The result is noise tolerant, and an experiment is motivated to distinguish the class of models ruled out from quantum theory.No-go theorems such as Bell's [1] are of central importance to our understanding of quantum mechanics. Bell's theorem shows that locally causal models must make different predictions from quantum theory. In addition to the fundamental significance of this result, Bell's theorem has applications in quantum information processing, most notably in deviceindependent cryptography and randomness generation [2][3][4][5].Recently, a number of new no-go results have been derived, addressing a different question than whether nature can be described by a locally causal theory. The question concerns whether the quantum state should be viewed as a description of the physical state of a system, or as an observer's information about the system. Many authors (see, e.g., Refs. [6][7][8], and references therein) have argued for the latter, pointing out, for example, that quantum collapse is analogous to Bayesian updating of a classical probability distribution when new data is obtained, or that the indistinguishability of nonorthogonal quantum states is analogous to the indistinguishability of overlapping probability distributions. Ref. [9], following Ref. [10], considers models of a specific form, in which the quantum state corresponds to a probability distribution over some set of underlying physical states, hence can be thought of as representing an observer's partial information about the physical state. It is shown that such models cannot recover the quantum predictions unless the distributions are disjoint for distinct quantum states. Roughly speaking, if the assumptions of Ref. [9] are accepted,...

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Introduction to Quantum Foundations

Ringbauer

2017

Exploring Quantum Foundations With Single Photons

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Maximally Epistemic Interpretations of the Quantum State and Contextuality

Cited by 86 publications

References 23 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

Noψ-Epistemic Model Can Fully Explain the Indistinguishability of Quantum States

Introduction to Quantum Foundations

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