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Chinese Physics B

Experimental simulation of violation of the Wright inequality by coherent light

Feng Zhu, Wei Zhang, Yidong Huang

Published Sep 1, 2017• 2 citations
Publisher

Abstract

In this paper, we investigate the simulation of violation of the Wright inequality by the classical optical experiment theoretically and experimentally. The feasibility of the simulation is demonstrated by theoretical analysis based on descriptions of the classical electrodynamics and quantum mechanics, respectively. Then, the simulation of violation of the Wright inequality is realized experimentally. The setup is based on a laser source, free-space optical devices and power meters. The experimental result violates the noncontextuality hidden variable bound, agreeing with the quantum bound. This method can be extended to other types of noncontextuality inequalities.

DOI
10.1088/1674-1056/26/10/100302

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In this paper, we investigate the simulation of violation of the Wright inequality by the classical optical experiment theoretically and experimentally. The feasibility of the simulation is demonstrated by theoretical analysis based on descriptions of the classical electrodynamics and quantum mechanics, respectively. Then, the simulation of violation of the Wright inequality is realized experimentally. The setup is based on a laser source, free-space optical devices and power meters. The experimental result violates the noncontextuality hidden variable bound, agreeing with the quantum bound. This method can be extended to other types of noncontextuality inequalities.
Elaborating on a previous work by Simon et al (2000 Phys. Rev. Lett. 85 1783) we propose a realizable quantum optical single-photon experiment using standard present day technology, capable of discriminating maximally between the predictions of quantum mechanics (QM) and noncontextual hidden variable theories (NCHV). Quantum mechanics predicts a gross violation (up to a factor of 2) of the noncontextual Bell-like inequality associated with the proposed experiment. An actual maximal violation of this inequality would demonstrate (modulo fair sampling) an all-or-nothing type contradiction between QM and NCHV.
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.
We report two fundamental experiments on three-level quantum systems (qutrits). The first one tests the simplest task for which quantum mechanics provides an advantage with respect to classical physics. The quantum advantage is certified by the violation of Wright's inequality, the simplest classical inequality violated by quantum mechanics. In the second experiment, we obtain contextual correlations by sequentially measuring pairs of compatible observables on a qutrit, and show the violation of Klyachko et al.'s inequality, the most fundamental noncontextuality inequality violated by qutrits. Our experiment tests exactly Klyachko et al.'s inequality, uses the same measurement procedure for each observable in every context, and shows that the violation does not depend on the order of the measurements.
Quantum contextuality provides a fundamental signature of nonclassical behavior that cannot be explained by noncontextual hidden-variable models. We propose and experimentally implement a linear-optical setup for demonstrating Kochen-Specker contextuality via a violation of the KCBS inequality using single photons. Our scheme employs sequential measurements realized with linear-optical networks and on-off photodetectors. The construction ensures that each co-measured observable is implemented by the same physical operation across different contexts. Our experimental results demonstrate a clear violation of the KCBS inequality and robustness against photon loss. Beyond fundamental investigations, the proposed setup provides a practical tool for probing non-classicality and photon-number statistics of quantum states, which in turn enables the verification of single-photon sources.
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.
Teaching quantum mechanics is challenging, not least because the theory often conflicts with our classical worldview. Quantum correlations in particular are notoriously counter-intuitive. Their non-classical behavior is typically revealed through Bell-type inequalities. Among these, Wigner's Inequality constitutes a particularly accessible test, as it relies on minimal set-theoretic assumptions. In this pedagogical paper, we derive Wigner's Inequality, describe a quantum-optical setup to experimentally violate it, and provide access to the raw data, enabling students and instructors to perform their own analyses. Our measured data shows clear violations of Wigner's Inequality, directly illustrating the non-classical nature of quantum correlations. By connecting theory, experiment, and data analysis, this paper equips educators with a resource for engaging students in authentic scientific practice and developing a deeper understanding of quantum systems.