Einstein, Incompleteness, and the Epistemic View of Quantum States

Harrigan, Nicholas; Spekkens, Robert W.

doi:10.1007/s10701-009-9347-0

Cited by 432 publications

(643 citation statements)

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“…[10], Definition 1. An ontological model is ψ-epistemic if there exists at least one pair of distinct quantum states, |ψ and |φ , such that the corresponding epistemic states µ ψ and µ φ have nonzero overlap, i.e., ω C (µ ψ , µ φ ) > 0.…”

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confidence: 99%

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

et al. 2014

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“…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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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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“…A precise formulation of these two alternatives, opening the way to clear-cut answers, was provided in [HS10]: if the wave-function corresponds to a real, ontic, property of physical systems, the preparation of a system in different pure quantum states should always result in different physical states. If, on the other hand, the wave-function has an epistemic status, such preparations should sometimes result in the same underlying physical state.…”

Section: Discussionmentioning

confidence: 99%

“…Following the formulation of Nicholas HARRIGAN and Robert W. SPEKKENS [HS10], the starting point is the assumption that every quantum system possesses a real physical state, generally called the ontic state, denoted λ. Somewhat similarly than in the Bell theorem (see sec-tion 1.2), we suppose that our present description of Nature could be incomplete, and that the real state λ of a physical system is not known to the present physics.…”

Section: ψ-Ontic and ψ-Epistemic Modelsmentioning

confidence: 99%

Manipulating Frequency Entangled Photons

Olislager

Cussey²,

Nguyễn

et al. 2010

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Serge, un immense merci pour m'avoir guidé tout au long de ces années, avec un équilibre parfait entre encadrement et liberté. Merci pour tes conseils avisés, ton éclectisme, ton enthousiasme. Merci pour les agréables moments en ta compagnie. Je ne comprends toujours pas comment tu peux annoncer 90% du temps "poker" tout en en faisant une stratégie gagnante.Philippe, un tout grand merci de m'avoir "ouvert les portes du laboratoire" et pour la confiance que tu m'as témoignée. Merci de faire régner la bonne ambiance au sein d'OPÉRA et pour ta gestion des dossiers kilométriques que ma thèse en co-tutelle a notamment imposés.Jean-Marc, merci pour ton expertise dans la manipulation de photons en fréquence. Tes connaissances au laboratoire, tes ressources et ta disponibilité ont grandement facilité les débuts de ma thèse. Rien n'aurait été possible sans toi.Kien, merci pour ton incroyable taux de génération de nouvelles idées (en particulier celle qui a initié ma thèse) et pour ton aide au jour le jour. Grâce à toi, je sais (presque correctement) faire des soudures électriques.Jean-Marc et Kien, je me souviendrai longtemps de notre première semaine de manipulations à Bruxelles. Merci aussi Johann pour cette chouette expérience d'insomnies scientifiques.Les mois passés à Besançon furent passionnants scientifiquement et agréables humainement. Qui a dit qu'il ne faisait jamais beau dans cette ville? Ismaël, merci pour tout le temps partagé autour d'une PublicationsThe present thesis is based on the following publications. IntroductionIn the twentieth century, the founding fathers of quantum mechanics explored the implications of their theory by designing gedanken experiments. In recent years, continuous improvement of the experimental manipulation of individual quantum systems has opened the way to exciting research, both on blackboards and in laboratories, and even towards field experiments.From the fundamental point of view, this progress allows to test the intrinsic quantum nature of microscopic systems, and how this connects to other scientific fields, such as metrology [GLM06]. Many of the gedanken experiments have now been performed experimentally. This includes tests of wave-particle duality, wave-function collapse, quantum nonlocality, etc.[Zei99, BLS + 13, Gis14]In a more applied direction, the manipulation of individual quantum systems is the basis for quantum information processing: when an information content is associated with transformations and measurements of quantum systems, it offers a new paradigm, full of potentialities, to information theory. This leads to quantum random number generation, quantum computing, quantum communication, including quantum teleportation and quantum cryptography, etc.[NC10]One of the promises of quantum information is the realization of a quantum internet [Kim08]: quantum communication links would allow to share quantum states between the nodesquantum computers-of the network [GT07]. Quantum cryptography and quantum teleportation would open the way to absolutely secure tr...

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Einstein, Incompleteness, and the Epistemic View of Quantum States

Cited by 432 publications

References 56 publications

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

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

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

Manipulating Frequency Entangled Photons

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