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Chinese Physics Letters

All-or-Nothing-Type Kochen-Specker Experiment with Thermal Lights

Xin-Bing Song, Hai-Bo Wang, Jun Xiong, Xiangdong Zhang

Published Nov 1, 2012• 3 citations
Publisher

Abstract

Recently, the Kochen—Specker theorem has been demonstrated and quantum contextuality has been observed experimentally by using special and independent quantum states. On the other hand, recent investigations have shown that a thermal light source can mimic the two-photon entangled source to perform the imaging effects. We perform an all-or-nothing—type Kochen-Specker experiment using the thermal light source and obtain the same results as those using quantum sources. The physical origin for such a phenomenon is analyzed.

DOI
10.1088/0256-307x/29/11/114214

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Recently, the Kochen—Specker theorem has been demonstrated and quantum contextuality has been observed experimentally by using special and independent quantum states. On the other hand, recent investigations have shown that a thermal light source can mimic the two-photon entangled source to perform the imaging effects. We perform an all-or-nothing—type Kochen-Specker experiment using the thermal light source and obtain the same results as those using quantum sources. The physical origin for such a phenomenon is analyzed.
We propose a feasible Kochen–Specker experiment with single photons, whose goal is to submit noncontextual hidden-variable theories to nonstatistical, all-or-nothing tests. Our proposal improves some recently performed tests in two respects. First, the present proposal is state-independent, thereby realizing a scheme designed by Cabello and García-Alcaine that was only partially realized in recent experiments. Second, our proposal can deal with non-ideal detectors without invoking the fair sampling assumption.
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.
We address the problem of deriving the set of quantum correlations for every Bell and Kochen-Specker (KS) contextuality scenario from simple assumptions. We show that the correlations that are possible according to quantum theory are equal to those possible under the assumptions that there is a nonempty set of correlations for every KS scenario and a statistically independent realization of any two KS experiments. The proof uses tools of the graph-theoretic approach to correlations and deals with Bell nonlocality and KS contextuality in a unified way.
The Kochen–Specker (KS) theorem reveals the nonclassicality of single quantum systems. In contrast, Bell's theorem and entanglement concern the nonclassicality of composite quantum systems. Accordingly, unlike incompatibility, entanglement and Bell non-locality are not necessary to demonstrate KS-contextuality. However, here we find that for multiqubit systems, entanglement and non-locality are both essential to proofs of the Kochen–Specker theorem. Firstly, we show that unentangled measurements (a strict superset of local measurements) can never yield a logical (state-independent) proof of the KS theorem for multiqubit systems. In particular, unentangled but nonlocal measurements—whose eigenstates exhibit ''nonlocality without entanglement"—are insufficient for such proofs. This also implies that proving Gleason's theorem on a multiqubit system necessarily requires entangled projections, as shown by Wallach [Contemp Math, 305: 291-298 (2002)]. Secondly, we show that a multiqubit state admits a statistical (state-dependent) proof of the KS theorem if and only if it can violate a Bell inequality with projective measurements. We also establish the relationship between entanglement and the theorems of Kochen–Specker and Gleason more generally in multiqudit systems by constructing new examples of KS sets. Finally, we discuss how our results shed new light on the role of multiqubit contextuality as a resource within the paradigm of quantum computation with state injection.