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Physical Review A

Experimental demonstration of quantum contextuality with nonentangled photons

Bi‐Heng Liu, Yun‐Feng Huang, Yan-Xiao Gong, Fang‐Wen Sun, Y. S. Zhang, Cheng Li, Guang‐Can Guo

Published Oct 1, 2009• 47 citations
Publisher

Abstract

We present an experimental test of quantum contextuality by using two-photon product states. The experimental results show that the noncontextual hidden-variable theories are violated by nonentangled states in spite of the local hidden-variable theories can be violated or not. We find that the Hong-Ou-Mandel-type quantum interference effect causes the quantum contextuality.

DOI
10.1103/physreva.80.044101

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We present an experimental test of quantum contextuality by using two-photon product states. The experimental results show that the noncontextual hidden-variable theories are violated by nonentangled states in spite of the local hidden-variable theories can be violated or not. We find that the Hong-Ou-Mandel-type quantum interference effect causes the quantum contextuality.
We show that correlations between the detector positions at the two-photon Young interference plane exhibit contextual behavior. Contextuality is demonstrated by showing the violation of the nnn-cycle noncontextuality inequalities [M. Ara\'ujo et al., Phys. Rev. A 88, 022118 (2013)] for any even number nnn of observables ranging from 4 to 14. These violations exclude noncontextual hidden-variable theories as an explanation of the conditional two-photon Young pattern. Unlike recent contextuality experiments, ours is free of the compatibility loophole.
The violation of contextuality inequalities shows a strong conflict between the noncontextual hidden variable theory and quantum mechanics. A single qutrit is the simplest indivisible quantum system that can allow a state-dependent contextuality test with five observables and a state-independent contextuality test with 13 observables. For any qutrit states, except for the maximally mixed state, one can always find a set of nine observables for which the corresponding inequality is violated [P. Kurzynski and D. Kaszlikowski, Phys. Rev. A 86, 042125 (2012)]. In this paper, we demonstrate the violation of this inequality using single-photon experiments. Our experiments not only enrich the tests of quantum contextuality, but also deepen the understanding of the physical nature of quantum mechanics.
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.
An experimental demonstration of quantum contextuality with neutrons is presented, which intended to exhibit a Kochen-Specker-like phenomenon. Since no perfect correlation is expected in practical experiments, inequalities are derived to distinguish quantitatively the obtained results from predictions by a noncontextual hidden variable theory. Experiments were accomplished with the use of a neutron interferometer combined with spinor manipulation devices. The results clearly violate the prediction of noncontextual theories.
We formulate stochastic noncontextual hidden-variable theories. In such theories the hidden state \ensuremath{\lambda} specifies not definite values, but expectation values A\ifmmode\bar\else\textasciimacron\fi{}(\ensuremath{\lambda}), . . . of observables A, . . . and noncontextuality means that A\ifmmode\bar\else\textasciimacron\fi{}(\ensuremath{\lambda}) is independent of which other commuting observables commuting with A are measured together with A. We show via Bell inequalities that such theories conflict with quantum theory and propose a two-photon experimental test. We also show that for a single particle of spin (2n{2}^{\mathit{n}}2n-1)/2, quantum violation of classical noncontextuality grows exponentially with n.