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Scientific Reports

State-independent contextuality in classical light

Tao Li, Qiang Zeng, Xiong Zhang, Tian Chen, Xiangdong Zhang

Published Nov 19, 2019• 6 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-019-51250-5

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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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We report a state-independent experimental test of quantum contextuality of a single-photon qutrit. The experimental results demonstrate violations of an inequality originally formulated by Yu and Oh [Phys. Rev. Lett. 108, 030402 (2012)] and further optimized by Cabello et al. [Phys. Rev. A 85, 032108 (2012)]; this inequality is satisfied by all noncontextual hidden variable models and is violated by all qutrit states. Our experiment shows quantum contextuality of this nature in a most fundamental way: A way that is independent of state and unrelated to entanglement.
Abstract Contextuality is a phenomenon at the heart of quantum mechanics different from classical behavior and has been recently identified as a resource in quantum information processing. Experimental demonstration of contextuality is thus an important goal. We experimentally demonstrate a test of state-independent contextuality in a four-dimensional Hilbert space with single photons and violate the inequality by at least 387 standard deviations. Despite imperfections and possible measurement disturbance, our results cannot be explained in non-contextual models. We also provide a theoretical analysis of a test of contextuality with a coherent light field and show how the definitions affect the emergence of non-classical correlations. Our result sheds new light on the conflict between quantum and classical physics.
Recent experiments have demonstrated ququart state-independent quantum contextuality and qutrit state-dependent quantum contextuality. So far, the most basic form of quantum contextuality pointed out by Kochen and Specker, and Bell, has eluded experimental confirmation. Here we present an experimentally feasible test to observe qutrit state-independent quantum contextuality using single photons in a three-path setup. In addition, we show that if the same measurements are performed on two entangled qutrits, rather than sequentially on the same qutrit, then the noncontextual inequality becomes a Bell inequality. We show that this connection also applies to other recently introduced noncontextual inequalities.
The contradiction between classical and quantum physics can be identified through quantum contextuality, which does not need composite systems or spacelike separation. Contextuality is proven either by a logical contradiction between the noncontextuality hidden variable predictions and those of quantum mechanics or by the violation of noncontextual inequality. We propose an experimental scheme of state-independent contextual inequality derived from the Mermin proof of the Kochen–Specker (KS) theorem in eight-dimensional Hilbert space, which could be observed either in an individual system or in a composite system. We also show how to resolve the compatibility problems. Our scheme can be implemented in optical systems with current experiment techniques.
The Clauser-Horne-Shimony-Holt (CHSH) inequality and the Klyachko-Can-Binicioglu-Shumovski (KCBS) inequality present a tradeoff on the no-disturbance (ND) principle. Recently, the fundamental monogamy relation between contextuality and nonlocality in quantum theory has been demonstrated experimentally. Here we show that such a relation and tradeoff can also be simulated in classical optical systems. Using polarization, path and orbital angular momentum of the classical optical beam, in classical optical experiment we have observed the stringent monogamy relation between the two inequalities by implementing the projection measurement. Our results show the application prospect of the concepts developed recently in quantum information science to classical optical system and optical information processing.