Simple Test for Hidden Variables in Spin-1 Systems

Klyachko, Alexander A.; Can, M. Ali; Binicioğlu, Sinem; Shumovsky, A.S.

doi:10.1103/physrevlett.101.020403

Cited by 510 publications

(742 citation statements)

References 27 publications

(24 reference statements)

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“…These papers were mainly focused on the CHSH scenario. The KlyachkoCan-Binicioǧlu-Shumovsky (KCBS) scenario [18] is currently the subject of active research. The CHSH and KCBS scenarios are respectively the n = 4 and n = 5 cases of the n-cycle scenario [19,20].…”

Section: Introductionmentioning

confidence: 99%

On generalized entropies and information-theoretic Bell inequalities under decoherence

Rastegin

2015

Annals of Physics

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We consider information-theoretic inequalities of the Bell type in the presence of decoherence. It is natural that too strong coupling with the environment can prevent an observation of quantum correlations. In this regard, the use of various entropic functions may give additional capabilities to reveal desired correlations. It was already shown that the Bell and Leggett-Garg inequalities in terms conditional Tsallis entropies are more sensitive in the cases of detection inefficiencies. In this paper, we study capabilities of generalized conditional entropies of the Tsallis type in analyzing the Bell theorem in decoherence scenarios. Two forms of the conditional Tsallis q-entropy are known in the literature. We show that each of them can be used for defining a metric in the probability space of interest. Such metrics can be used in realizing the so-called triangle principle. The triangle principle has recently been proposed as a unifying approach to questions of local realism and noncontextuality. Applying the triangle principle leads to the two families of q-metric inequalities of the Bell type. Information-theoretic formulations in terms of the q-entropic metrics are first discussed for the CHSH scenario in dephasing environment. Then we also revisit q-entropic inequalities of the Leggett-Garg type. An environmental influence is modeled by the phase damping channel and by the depolarizing channel.

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Section: Introductionmentioning

confidence: 99%

On generalized entropies and information-theoretic Bell inequalities under decoherence

Rastegin

2015

Annals of Physics

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“…This third approach is based on two observations: on one hand, that quantum contextual correlations, i.e., quantum correlations for compatible (but not necessarily spacelike compatible) measurements provide a natural generalization of quantum nonlocal correlations that leaves room for a wider range of experimental scenarios, including systems that cannot be separated into parts or represented as tensor product of smaller spaces [18,[24][25][26][27][28] and for systems prepared in arbitrary quantum states [19,[25][26][27][29][30][31][32]. The second observation comes from the graph approach to quantum correlations introduced in Ref.…”

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confidence: 99%

“…When applied to the OR product of two copies of the exclusivity graph (which may be seen as two copies of the same experiment), the E principle singles out the maximum quantum value for experiments whose exclusivity graphs are vertex-transitive and self-complementary [20], which include the simplest NC inequality violated by QT, namely the Klyachko-CanBinicioglu-Shumovsky (KCBS) inequality [18]. Moreover, either applied to two copies of the exclusivity graph of the Clauser-Horne-Shimony-Holt (CHSH) [39] Bell inequality [14] or of a simpler inequality [20], the E principle excludes Popescu-Rohrlich nonlocal boxes [6] and provides an upper bound to the maximum violation of the CHSH inequality which is close to the Tsirelson bound [40].…”

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confidence: 99%

“…The exclusivity graphs of many interesting inequalities including CHSH [39], KCBS [18], the n−cycle inequalities [22,33,41,42], and the antihole inequalities [22] are vertex-transitive. A graph is vertex-transitive if for any pair u, v ∈ V (G) there is φ ∈ Aut(G) such that v = φ(u), where Aut(G) is the group of automorphisms of G (i.e., the permutations ψ of the set of vertices such that u, v ∈ V (G) are adjacent if and only if ψ(u), ψ(v) are adjacent).…”

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confidence: 99%

“…A second approach consists of identifying principles that explain the set of quantum nonlocal correlations [6][7][8][9][10][11][12][13][14]. The third approach consists of identifying principles that explain the set of quantum contextual correlations [15][16][17][18][19] without restrictions imposed by a specific experimental scenario [20][21][22][23].…”

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confidence: 99%

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Exclusivity principle forbids sets of correlations larger than the quantum set

2014

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We show that the exclusivity (E) principle singles out the set of quantum correlations associated to any exclusivity graph assuming the set of quantum correlations for the complementary graph. Moreover, we prove that, for self-complementary graphs, the E principle, by itself (i.e., without further assumptions), excludes any set of correlations strictly larger than the quantum set. Finally, we prove that, for vertex-transitive graphs, the E principle singles out the maximum value for the quantum correlations assuming only the quantum maximum for the complementary graph. This opens the door for testing the impossibility of higher-than-quantum correlations in experiments. Introduction.-One of the most seductive scientific challenges in recent times is deriving quantum theory (QT) from first principles. The starting point is assuming general probabilistic theories allowing for correlations that are more general than those that arise in QT, and the goal is to find principles that pick out QT from this landscape of possible theories.

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The Negativity‐to‐Violation Map between Wigner Function and Quantum Contextuality Inequality for a Single Qudit

Huang

Zhang

2019

Annalen der Physik

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The relation between discrete Wigner function and quantum contextuality based on graph theory has been studied, following the work in [Nature 510,351(2014)]. To do this, non-stabilizer projectors have been introduced to a series of non-contextuality graphs based on stabilizer projectors for a single qudit with odd prime dimension. It has been found that, for a phase space point defined by Wootters, there exists a given set of states for an odd-prime qudit where the negative discrete Wigner function on the phase space point means its quantum contextuality under measurements on the graphs designed by a specific method. To implement this method, a subset of non-stabilizer projectors has been found. In the union of the set of states for all phase space points, there exists a negativity-to-violation map between Wigner function and quantum contextuality inequality. The robustness of the equivalence under depolarizing noise has been analyzed and discussed. For demonstration purposes, the graphs with different independence numbers and the corresponding set of states have been established on a single qutrit. Different to the cited work, this method involves only a single qudit, then is experimentally feasible for a qutrit.

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Simple Test for Hidden Variables in Spin-1 Systems

Cited by 510 publications

References 27 publications

On generalized entropies and information-theoretic Bell inequalities under decoherence

On generalized entropies and information-theoretic Bell inequalities under decoherence

Exclusivity principle forbids sets of correlations larger than the quantum set

The Negativity‐to‐Violation Map between Wigner Function and Quantum Contextuality Inequality for a Single Qudit

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