dc.contributor.author | Liang, Yeong-Cherng | |
dc.contributor.author | Spekkens, Robert W | |
dc.contributor.author | Wiseman, Howard M | |
dc.date.accessioned | 2018-06-20T01:30:17Z | |
dc.date.available | 2018-06-20T01:30:17Z | |
dc.date.issued | 2011 | |
dc.date.modified | 2012-06-14T22:32:50Z | |
dc.identifier.issn | 0370-1573 | |
dc.identifier.doi | 10.1016/j.physrep.2011.05.001 | |
dc.identifier.uri | http://hdl.handle.net/10072/42574 | |
dc.description.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 entr饠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. | |
dc.description.peerreviewed | Yes | |
dc.description.publicationstatus | Yes | |
dc.format.extent | 752538 bytes | |
dc.format.mimetype | application/pdf | |
dc.language | English | |
dc.language.iso | eng | |
dc.publisher | Elsevier | |
dc.publisher.place | Netherlands | |
dc.relation.ispartofstudentpublication | N | |
dc.relation.ispartofpagefrom | 1 | |
dc.relation.ispartofpageto | 39 | |
dc.relation.ispartofissue | 1-2 | |
dc.relation.ispartofjournal | Physics Reports | |
dc.relation.ispartofvolume | 506 | |
dc.rights.retention | Y | |
dc.subject.fieldofresearch | Mathematical sciences | |
dc.subject.fieldofresearch | Physical sciences | |
dc.subject.fieldofresearch | Quantum information, computation and communication | |
dc.subject.fieldofresearch | Quantum optics and quantum optomechanics | |
dc.subject.fieldofresearch | Quantum physics not elsewhere classified | |
dc.subject.fieldofresearchcode | 49 | |
dc.subject.fieldofresearchcode | 51 | |
dc.subject.fieldofresearchcode | 510803 | |
dc.subject.fieldofresearchcode | 510804 | |
dc.subject.fieldofresearchcode | 510899 | |
dc.title | Specker's parable of the overprotective seer: A road to contextuality, nonlocality and complementarity | |
dc.type | Journal article | |
dc.type.description | C1 - Articles | |
dc.type.code | C - Journal Articles | |
gro.rights.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. | |
gro.date.issued | 2011 | |
gro.hasfulltext | Full Text | |
gro.griffith.author | Wiseman, Howard M. | |