Quantum Contextuality in a Single-Neutron Optical Experiment

Hasegawa, Yuji; Loidl, Rudolf; Badurek, G.; Baron, M.; Rauch, H.

doi:10.1103/physrevlett.97.230401

Cited by 153 publications

(106 citation statements)

References 28 publications

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“…They were implemented for 4-dim systems with photons [13][14][15][16][17][18], neutrons [19][20][21] trapped ions [22], and molecular nuclear spins in the solid states [23], for 6-dim systems via six path possibilities for the photon transmission through a diffractive aperture [24,25], and for 8-dim systems by means of the linear transverse momentum of single photons transmitted by diffractive apertures addressed in spatial light modulators [26].…”

Section: Introductionmentioning

confidence: 99%

Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

Pavičić¹

2017

Phys. Rev. A

124

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Quantum contextuality turns out to be a necessary resource for universal quantum computation and important in the field of quantum information processing. It is therefore of interest both for theoretical considerations and for experimental implementation to find new types and instances of contextual sets and develop methods of their optimal generation. We present an arbitrary exhaustive hypergraph-based generation of the most explored contextual sets-Kochen-Specker (KS) ones-in 4, 6, 8, 16, and 32 dimensions. We consider and analyse twelve KS classes and obtain numerous properties of theirs, which we then compare with the results previously obtained in the literature. We generate several thousand times more types and instances of KS sets than previously known. All KS sets in three of the classes and in the upper part of a fourth are novel. We make use of the MMP hypergraph language, algorithms, and programs to generate KS sets strictly following their definition from the Kochen-Specker theorem. This approach proves to be particularly advantageous over the parity-proof-based ones (which prevail in the literature), since it turns out that only a very few KS sets have a parity proof (in six KS classes < 0.01% and in one of them 0%). MMP hypergraph formalism enables a translation of an exponentially complex task of solving systems of nonlinear equations, describing KS vector orthogonalities, into a statistically linearly complex task of evaluating vertex states of hypergraph edges, thus exponentially speeding up the generation of KS sets and enabling us to generate billions of novel instances of them. The MMP hypergraph notation also enables us to graphically represent KS sets and to visually discern their features.

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Section: Introductionmentioning

confidence: 99%

Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

Pavičić¹

2017

Phys. Rev. A

124

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“…Experimental tests of noncontextual HV theories have been carried out with photons [35][36][37][38]46], neutrons [37,38], lasercooled trapped ions [45], and liquid-state nuclear magnetic resonance systems [48]. In the experiments with photons and neutrons, single particles were prepared and measured in a four-dimensional state space composed of two twodimensional state spaces describing the particle's polarization and the path it was following.…”

Section: Experimental Implementationmentioning

confidence: 99%

“…Nevertheless, first experiments have been performed, but these experiments required some additional assumptions [35][36][37][38]. Furthermore, the notion of contextuality has been extended to state preparations [39] and experimentally investigated [40].…”

Section: Introductionmentioning

confidence: 99%

Compatibility and noncontextuality for sequential measurements

et al. 2010

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A basic assumption behind the inequalities used for testing noncontextual hidden variable models is that the observables measured on the same individual system are perfectly compatible. However, compatibility is not perfect in actual experiments using sequential measurements. We discuss the resulting "compatibility loophole" and present several methods to rule out certain hidden variable models that obey a kind of extended noncontextuality. Finally, we present a detailed analysis of experimental imperfections in a recent trapped-ion experiment and apply our analysis to that case.

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confidence: 99%

“…Now, if one maintains realistic omniscience -that is, the pre-existence of all outcomes of complementary potential observables -then it is indeed true that, as stated by Cabello [6], "the immense majority of the experimental violations of Bell inequalities [[proves]] quantum contextuality." Actually, the only difference between older evidence of violations of Bell-type inequalities and more recent ones [7][8][9][10] seems to be based on the fact that the prior ones rely on spatially separated quanta in EinsteinPodolsky-Rosen "explosion" type schemes, whereas more recent ones are based on single quanta -a concept which appears to be more in the spirit of Kochen-Specker type theorems which apply to the structure of observables of single quanta [11]. But even these sorts of empirical findings referring to single quanta rely on the noninstantaneous measurement of all but a few (mostly two or three in cases involving two-or three-particle EinsteinPodolsky-Rosen and Greenberger-Horne-Zeilinger type) configurations, and therefore cannot even counterfactually assure the operational existence of all elements of physical reality at once [12].…”

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confidence: 99%

Haunted Quantum Contextuality versus Value Indefiniteness

Svozil¹

2012

Computation, Physics and Beyond

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Physical entities are ultimately (re)constructed from elementary yes/no events, in particular clicks in detectors or measurement devices recording quanta. Recently, the interpretation of certain such clicks has given rise to unfounded claims which are neither necessary nor sufficient, although they are presented in that way. In particular, clicks can neither inductively support nor "(dis)prove" the Kochen-Specker theorem, which is a formal result that has a deductive proof by contradiction. More importantly, the alleged empirical evidence of quantum contextuality, which is "inferred" from violations of bounds of classical probabilities by quantum correlations, is based on highly nontrivial assumptions, in particular on physical omniscience. Time and again, in coffee houses and elsewhere, members of the Viennese experimental physics community reminded me always to keep in mind that all our physical "facts" are ultimately derived and constructed from detector clicks. It is this basic wisdom that, when consequentially applied to recent experiments, suggests to rethink certain claims of empirical proof.Let us, for the sake of properly assessing the situation, review some historical cornerstones. Motivated by certain, as it turned out inapplicable, no-go theorems by von Neumann regarding hidden parameters, Bell came forward with criteria for classical probabilities and expectations, resembling the conditions of possible experience that had been contemplated by Boole a century earlier [1]. Essentially, these criteria state that, if one forces the (counterfactual) physical co-existence upon certain finite sets of complementary, incompatible, potential observables -meaning that every single one could be measured, although due to complementarity it is impossible to simultaneously measure all of them -the associated potential measurement outcomes are subject to certain algebraic bounds.As these probabilistic bounds are not satisfied by quantum observables, the respective measurements outcomes cannot consistently co-exist [2]; at least not under the classical presumptions entering the calculations leading to these bounds. These arguments have subsequently been strengthened by the Kochen-Specker and the Greenberger-Horne-Zeilinger theorems, as for the latter ones any violations of the conditions of possible experience must occur on every single quantum and at least for a single observable [3] rather than occasionally.Those results relate to situations in which omniscience is assumed; that is, all observables which could potentially be observed can indeed be associated with actual elements of physical reality of a single quantum. For a realist this might appear self-evident [4]. Also for experimentalists this seems to be obvious; after all, any particular observation renders outcomes, regardless of the mutual complementarity of some of the observables involved; in this view, "potentially operational" means "existence." By this inkling, the situation suggests that the measurement "reveals" a pre-existing element of physical r...

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Quantum Contextuality in a Single-Neutron Optical Experiment

Cited by 153 publications

References 28 publications

Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

Compatibility and noncontextuality for sequential measurements

Haunted Quantum Contextuality versus Value Indefiniteness

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