Experimental Implementation of a Kochen-Specker Set of Quantum Tests

D’Ambrosio, Vincenzo; Herbauts, Isabelle; Amselem, Elias; Nagali, Eleonora; Bourennane, Mohamed; Sciarrino, Fabio; Cabello, Adán

doi:10.1103/physrevx.3.011012

Cited by 86 publications

(116 citation statements)

References 59 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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“…(6) and (5), respectively, for all odd numbers of spins from N = 3 to 17. Note that the pair of forbidden projectors Π (5) 0 and Π (13) 0 have the remarkable geometric property that first order errors vanish when Z w = i, explaining the small statistical standard deviation σ observed in the experimental data. The cho- sen witnesses for other N in Fig.…”

Section: Resultsmentioning

confidence: 97%

“…Unlike the implicit global contradictions inherent to existing BKS experiments [11][12][13], our method confines the apparent contradiction to a particular context, where its physical consequences may be explicitly revealed through weak measurements. Notably, unlike existing approaches to demonstrating BKS-contextuality [27], our witness does not require entangled preparations or measurements, or indeed any interaction between the different spins at all.…”

Section: Discussionmentioning

confidence: 99%

Confined contextuality in neutron interferometry: Observing the quantum pigeonhole effect

et al. 2017

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Previous experimental tests of quantum contextuality based on the Bell-Kochen-Specker (BKS) theorem have demonstrated that not all observables among a given set can be assigned noncontextual eigenvalue predictions, but have never identified which specific observables must fail such assignment. We now remedy this shortcoming by showing that BKS contextuality can be confined to particular observables by pre-and postselection, resulting in anomalous weak values that we measure using modern neutron interferometry. We construct a confined contextuality witness from weak values, which we measure experimentally to obtain a 5σ average violation of the noncontextual bound, with one contributing term violating an independent bound by more than 99σ. This weakly measured confined BKS contextuality also confirms the quantum pigeonhole effect, wherein eigenvalue assignments to contextual observables apparently violate the classical pigeonhole principle.

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“…This degree of freedom is related to the spatial modes of electromagnetic radiation and provides an infinite dimensional Hilbert space that allows us to implement qudits of, in principle, arbitrary d using single photons. OAM is attracting great attention in the last decade for its applications in a va- riety of disciplines such as biophysics [21][22][23], metrology [24], astronomy [25], quantum communication [26,27], and fundamental quantum physics [28,29]. Here we take advantage of the wide alphabet provided by OAM to encode six-dimensional single photon quantum states by choosing as a logical basis the following OAM eigenstates subset:…”

mentioning

confidence: 99%

Device-Independent Certification of High-Dimensional Quantum Systems

et al. 2014

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An important problem in quantum information processing is the certification of the dimension of quantum systems without making assumptions about the devices used to prepare and measure them, that is, in a device-independent manner. A crucial question is whether such certification is experimentally feasible for high-dimensional quantum systems. Here we experimentally witness in a device-independent manner the generation of six-dimensional quantum systems encoded in the orbital angular momentum of single photons and show that the same method can be scaled, at least, up to dimension 13. Introduction.-Dimensionality is a fundamental property of physical systems and a key resource in quantum information processing. Phenomena such as contextuality require systems of a certain minimum dimension to occur [1,2]; applications such as quantum secure communication have different levels of security depending on the dimension of the systems [3,4], and methods to characterize quantum states strongly depend on the assumed dimension of the systems [5]. It is therefore of crucial importance to develop methods to certify whether a source produces systems that have at least a certain dimension and to distinguish quantum systems from classical systems of the same dimension. The first theoretical tools for providing lower bounds on the dimension of quantum systems were based on Bell inequalities [6,7] and random access codes [8].

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Experimental Implementation of a Kochen-Specker Set of Quantum Tests

Cited by 86 publications

References 59 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

Confined contextuality in neutron interferometry: Observing the quantum pigeonhole effect

Device-Independent Certification of High-Dimensional Quantum Systems

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