Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Scientific Reports

Two Fundamental Experimental Tests of Nonclassicality with Qutrits

Johan Ahrens, Elias Amselem, Adán Cabello, Mohamed Bourennane

Published Jul 10, 2013• 51 citations
Publisher

Abstract

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 implements the sequential measurements in any possible order.

DOI
10.1038/srep02170

Related papers

Two Fundamental Experimental Tests of Nonclassicality with Qutrits

Johan Ahrens, Elias Amselem, Adán Cabello +1 more

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.

arXiv:1301.2887•Jan 14, 2013•1 citation

Comment on "Two Fundamental Experimental Tests of Nonclassicality with Qutrits"

Radek Łapkiewicz, Li, Peizhe, Christoph Schaeff +4 more

In a recent paper [arXiv:1301.2887] Ahrens et al. claim that our "(...) experiment on qutrits does not test Klyachko et al.'s inequality, but an inequality with extra correlations" and that the "(...) experiment cannot be considered a proper test of a noncontextuality inequality, since the same observable is measured with different setups in different contexts". We disagree with these claims. In this note we briefly re-state how our test of the non-contextuality inequality was constructed. We explain how we keep the context of measurements when switching between different terms of the tested inequality, and we argue that we did in fact test the Klyachko, Can, Binicioglu and Shumovsky inequality. In doing so, we also clarify why our experiment is indeed a proper test of noncontextual realism.

arXiv:1305.5529•May 23, 2013•5 citations

Experimental demonstration of quantum contextuality with nine observables on a single photonic qutrit

Xiao-Xiao Chen, Jian Li, Mairikena Aili +3 more

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.

Physical Review A•Apr 25, 2023•2 citations

Probing the limits of correlations in an indivisible quantum system

Maciej Malinowski, Chi Zhang, Florian Leupold +3 more

We employ a trapped ion to study quantum contextual correlations in a single qutrit using the 5-observable Klyachko, Can, Binicio\ifmmode \breve{g}\else \u{g}\fi{}lu, and Shumovsky inequality, which is arguably the most fundamental noncontextuality inequality for testing quantum mechanics (QM). We quantify the effect of systematics in our experiment by purposely scanning the degree of signaling between measurements, which allows us to place realistic bounds on the nonclassicality of the observed correlations. Our results violate the classical bound for this experiment by up to 25 standard deviations, while being in agreement with the QM limit. In order to test the prediction of QM that the contextual fraction increases with the number of observables, we gradually increase the complexity of our measurements from 5 up to 121 observables. We find stronger-than-classical correlations in all prepared scenarios up to 101 observables, beyond which experimental imperfections blur the quantum-classical divide.

arXiv:1712.06494•Physical Review A•Nov 16, 2018•22 citations

Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality

Adán Cabello, Elias Amselem, Kate Blanchfield +2 more

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.

arXiv:1203.0981•Physical Review A•Mar 5, 2012•37 citations

Linear-optical test of quantum contextuality with sequential measurements

Jiaqi Liu, Bita Olamaei, Lijian Zhang +2 more

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.

quant-pharXiv:2605.18112•May 19, 2026•0 citations
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 implements the sequential measurements in any possible order.
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.
In a recent paper [arXiv:1301.2887] Ahrens et al. claim that our "(...) experiment on qutrits does not test Klyachko et al.'s inequality, but an inequality with extra correlations" and that the "(...) experiment cannot be considered a proper test of a noncontextuality inequality, since the same observable is measured with different setups in different contexts". We disagree with these claims. In this note we briefly re-state how our test of the non-contextuality inequality was constructed. We explain how we keep the context of measurements when switching between different terms of the tested inequality, and we argue that we did in fact test the Klyachko, Can, Binicioglu and Shumovsky inequality. In doing so, we also clarify why our experiment is indeed a proper test of noncontextual realism.
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 employ a trapped ion to study quantum contextual correlations in a single qutrit using the 5-observable Klyachko, Can, Binicio\ifmmode \breve{g}\else \u{g}\fi{}lu, and Shumovsky inequality, which is arguably the most fundamental noncontextuality inequality for testing quantum mechanics (QM). We quantify the effect of systematics in our experiment by purposely scanning the degree of signaling between measurements, which allows us to place realistic bounds on the nonclassicality of the observed correlations. Our results violate the classical bound for this experiment by up to 25 standard deviations, while being in agreement with the QM limit. In order to test the prediction of QM that the contextual fraction increases with the number of observables, we gradually increase the complexity of our measurements from 5 up to 121 observables. We find stronger-than-classical correlations in all prepared scenarios up to 101 observables, beyond which experimental imperfections blur the quantum-classical divide.
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.
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.