Specker’s parable of the overprotective seer: A road to contextuality, nonlocality and complementarity

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Title Specker’s parable of the overprotective seer: A road to contextuality, nonlocality and complementarity
Author Liang, Yeong-Cherng; Spekkens, Robert W.; Wiseman, Howard Mark
Journal Name Physics Reports
Year Published 2011
Place of publication Netherlands
Publisher Elsevier B.V.
Abstract In 1960, the mathematician Ernst Specker described a simple example of nonclassical correlations, the counter-intuitive features of which he dramatized using a parable about a seer, who sets an impossible prediction task to his daughter’s suitors. We revisit this example here, using it as an entrée to three central concepts in quantum foundations: contextuality, Bell-nonlocality, and complementarity. Specifically, we show that Specker’s parable offers a narrative thread that weaves together a large number of results, including the following: the impossibility of measurement-noncontextual and outcome-deterministic ontological models of quantum theory (the 1967 Kochen–Specker theorem), in particular, the recent state-specific pentagram proof of Klyachko; the impossibility of Bell-local models of quantum theory (Bell’s theorem), especially the proofs by Mermin and Hardy and extensions thereof; the impossibility of a preparation-noncontextual ontological model of quantum theory; the existence of triples of positive operator valued measures (POVMs) that can be measured jointly pairwise but not triplewise. Along the way, several novel results are presented: a generalization of a theorem by Fine connecting the existence of a joint distribution over outcomes of counterfactual measurements to the existence of a measurement-noncontextual and outcome-deterministic ontological model; a generalization of Klyachko’s proof of the Kochen–Specker theorem from pentagrams to a family of star polygons; a proof of the Kochen–Specker theorem in the style of Hardy’s proof of Bell’s theorem (i.e., one that makes use of the failure of the transitivity of implication for counterfactual statements); a categorization of contextual and Bell-nonlocal correlations in terms of frustrated networks; a derivation of a new inequality testing preparation noncontextuality; some novel results on the joint measurability of POVMs and the question of whether these can be modeled noncontextually. Finally, we emphasize that Specker’s parable of the overprotective seer provides a novel type of foil to quantum theory, challenging us to explain why the particular sort of contextuality and complementarity embodied therein does not arise in a quantum world.
Peer Reviewed Yes
Published Yes
Alternative URI http://dx.doi.org/10.1016/j.physrep.2011.05.001
Copyright Statement Copyright 2011 Elsevier. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
Volume 506
Issue Number 1-2
Page from 1
Page to 39
ISSN 0370-1573
Date Accessioned 2011-09-21
Date Available 2012-06-14T22:32:50Z
Language en_US
Research Centre Centre for Quantum Dynamics
Faculty Faculty of Science, Environment, Engineering and Technology
Subject Quantum Information, Computation and Communication; Quantum Optics; Quantum Physics
URI http://hdl.handle.net/10072/42574
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1

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