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arXiv:1209.3831 · Physical Review Letters

State-Independent Experimental Test of Quantum Contextuality with a Single Trapped Ion

Xiang Zhang, Mark Um, Junhua Zhang, Shuoming An, Ye Wang, Dong-Ling Deng, Chao Shen, L.-M. Duan, Kihwan Kim

Published Feb 11, 2013• 86 citations
arXivHTMLPDF

Abstract

Using a single trapped ion, we have experimentally demonstrated state-independent violation of a recent version of the Kochen-Specker inequality in a three-level system (qutrit) that is intrinsically indivisible. Three ground states of the (171)Yb(+) ion representing a qutrit are manipulated with high fidelity through microwaves and detected with high efficiency through a two-step quantum jump technique. Qutrits constitute the most fundamental system to show quantum contextuality and our experiment represents the first one that closes the detection efficiency loophole for experimental tests of quantum contextuality in such a system.

DOI
10.1103/physrevlett.110.070401

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Using a single trapped ion, we have experimentally demonstrated state-independent violation of a recent version of the Kochen-Specker inequality in a three-level system (qutrit) that is intrinsically indivisible. Three ground states of the (171)Yb(+) ion representing a qutrit are manipulated with high fidelity through microwaves and detected with high efficiency through a two-step quantum jump technique. Qutrits constitute the most fundamental system to show quantum contextuality and our experiment represents the first one that closes the detection efficiency loophole for experimental tests of quantum contextuality in such a system.
Quantum contextuality, as proved by Kochen and Specker, and also by Bell, should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified. However, for the simplest system capable of exhibiting contextuality, a qutrit, the quantum contextuality is verified only state dependently in experiment because too many (at least 31) observables are involved in all the known state-independent tests. Here we report an experimentally testable inequality involving only 13 observables that is satisfied by all noncontextual realistic models while being violated by all qutrit states. Thus our inequality facilitates a state-independent test of the quantum contextuality for an indivisible quantum system. We also provide a record-breaking state-independent proof of the Kochen-Specker theorem with 13 directions determined by 26 points on the surface of a magic cube.
Quantum measurements cannot be thought of as revealing preexisting results, even when they do not disturb any other measurement in the same trial. This feature is called contextuality and is crucial for the quantum advantage in computing. Here, we report the observation of quantum contextuality simultaneously free of the detection, sharpness, and compatibility loopholes. The detection and sharpness loopholes are closed by adopting a hybrid two-ion system and highly efficient fluorescence measurements offering a detection efficiency of 100% and a measurement repeatability of >98%. The compatibility loophole is closed by targeting correlations between observables for two different ions in a Paul trap, a 171 Yb + ion and a 138 Ba + ion, chosen so measurements on each ion use different operation laser wavelengths, fluorescence wavelengths, and detectors. The experimental results show a violation of the bound for the most adversarial noncontextual models and open a way to certify quantum systems.
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.
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 intrinsic unpredictability of measurements in quantum mechanics can be used to produce genuine randomness. Here, we demonstrate a random number generator where the randomness is certified by quantum contextuality in connection with the Kochen-Specker theorem. In particular, we generate random numbers from measurements on a single trapped ion with three internal levels, and certify the generated randomness by showing a bound on the minimum entropy through observation of violation of the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality. Concerning the test of the KCBS inequality, we close the detection efficiency loophole for the first time and make it relatively immune to the compatibility loophole. In our experiment, we generate 1 × 10(5) random numbers that are guaranteed to have 5.2 × 10(4) bits of minimum entropy with a 99% confidence level.
Quantum mechanics implies that not all physical properties can be simultaneously well defined, such as the momentum and position due to Heisenberg uncertainty principle. Some alternative theories have been explored, notably the non-contextual hidden variable theories in which the properties of a system have pre-defined values which are independent of the measurement contextual. However, the Kochen-Specker theorem showed that such non-contextual hidden variable theories are in conflict with quantum mechanics. Recently, a state-independent inequality satisfied by non-contextual hidden variable theories and violated by quantum mechanics is proposed in the simplest three-state system (a qutrit) by the least 13 projection measurement rays. Here, we report an experimental demonstration of the violation of this inequality. This provides a state-independent experimental test of quantum contextuality, for the first time in solid state system, by a natural qutrit of nitrogen-vacancy center in diamond at room temperature.