Kochen–Specker theorem for a three-qubit system: A state-dependent proof with seventeen rays

Toh, Sing Poh; Zainuddin, Hishamuddin

doi:10.1016/j.physleta.2010.10.022

Cited by 3 publications

(2 citation statements)

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“…Kochen and Specker constructed a set of 117 vectors for which no consistent choice of colours could be made. The theorem has later been derived for larger Hilbert spaces and with fewer basis vectors [28][29][30][31][32][33][34][35], and has been generalized to open quantum systems [36,37].…”

Section: The Kochen-specker Theoremmentioning

confidence: 99%

On the connection between the theorems of Gleason and of Kochen and Specker

Marzlin

Landry

2015

Can. J. Phys.

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We present an elementary proof of a reduced version of Gleason's theorem and the Kochen-Specker theorem to provide a novel perspective on the relation between both theorems. The proof is based on a set of linear equations for the values of a function m on the unit sphere. In the case of Gleason's theorem the entire unit sphere needs to be considered, while a finite set of points suffices to prove the Kochen-Specker theorem.

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Section: The Kochen-specker Theoremmentioning

confidence: 99%

On the connection between the theorems of Gleason and of Kochen and Specker

Marzlin

Landry

2015

Can. J. Phys.

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“…The original theory needs 117 tests in dimension d = 3, and it is complex and nearly impossible to demonstrate experimentally. Afterwards the theory is simplified by many researchers 2 3 4 5 6 7 . These simplified contextuality theories have been tested experimentally, for instance in photon 8 9 10 11 12 13 , neutron 14 15 , trapped ion 16 and nuclear magnetic resonance 17 18 systems.…”

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confidence: 99%

Experimental contextuality in classical light

Zeng

Song

et al. 2017

Sci Rep

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The Klyachko, Can, Binicioglu, and Shumovsky (KCBS) inequality is an important contextuality inequality in three-level system, which has been demonstrated experimentally by using quantum states. Using the path and polarization degrees of freedom of classical optics fields, we have constructed the classical trit (cetrit), tested the KCBS inequality and its geometrical form (Wright’s inequality) in this work. The projection measurement has been implemented, the clear violations of the KCBS inequality and its geometrical form have been observed. This means that the contextuality inequality, which is commonly used in test of the conflict between quantum theory and noncontextual realism, may be used as a quantitative tool in classical optical coherence to describe correlation characteristics of the classical fields.

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State-independent contextuality in classical light

Zeng

Zhang

et al. 2019

Sci Rep

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State-independent contextuality is a fundamental phenomenon in quantum mechanics, which has been demonstrated experimentally in different systems in recent years. Here we show that such contextuality can also be simulated in classical optical systems. Using path and polarization degrees of freedom of classical optics fields, we have constructed the classical trit (cetrit), here the term ‘cetrit’ is the classical counterpart of a qutrit in quantum systems. Furthermore, in classical optical systems we have simulated the violations of several Yu-Oh-like noncontextual inequalities in a state-independent manner by implementing the projection measurements. Our results not only provide new physical insights into the contextuality and also show the application prospects of the concepts developed recently in quantum information science to classical optical systems and optical information processes.

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Kochen–Specker theorem for a three-qubit system: A state-dependent proof with seventeen rays

Cited by 3 publications

References 10 publications

On the connection between the theorems of Gleason and of Kochen and Specker

On the connection between the theorems of Gleason and of Kochen and Specker

Experimental contextuality in classical light

State-independent contextuality in classical light

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