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International Conference on Quantum, Nano and Micro Technologies (ICQNM)

Experimentally Testable State-Independent Violation of Bell-Type Inequalities for Quantum Contextuality

Adán Cabello

Published Feb 1, 2009• 0 citations
Publisher

Abstract

There are experimentally testable correlation Bell inequalities which are satisfied by any noncontextual theory but are violated by any quantum state. We discuss how to test one of them.
DOI
10.1109/icqnm.2009.36

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We show that, for any system with a number of levels which can be identified with nnn qubits, there is an inequality for the correlations between three compatible dichotomic measurements which must be satisfied by any noncontextual theory, but is violated by any quantum state. Remarkably, the violation grows exponentially with nnn, and the tolerated error per correlation also increases with nnn, showing that state-independent quantum contextuality is experimentally observable in complex systems.
Quantum correlations are contextual yet, in general, nothing prevents the existence of even more contextual correlations. We identify and test a noncontextuality inequality in which the quantum violation cannot be improved by any hypothetical postquantum theory, and use it to experimentally obtain correlations in which the fraction of noncontextual correlations is less than 0.06. Our correlations are experimentally generated from the results of sequential compatible tests on a four-state quantum system encoded in the polarization and path of a single photon.
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 view that non-classical phenomena are witnessed when noncontextuality inequalities are violated by quantum correlations has become widespread over the last decades, and many authors describe contextuality as a counter-intuitive and non-classical feature of quantum systems. In this paper we show that a classical input/output device generating contextual data (i.e., data violating noncontextuality inequalities) can easily be found if the following conditions are satisfied: (1) We only have access to a specific collection of epistemic measurements, namely measurements which do not necessarily reveal properties possessed by the system to the agent, and (2) not all these measurements can be jointly performed. The conclusion we draw from this example is twofold. Firstly, regarding model-independent contextuality, it suggests that, unlike Bell inequalities (whose violation allegedly implies non-locality), noncontextuality inequalities have no phenomenological significance per se: we cannot treat experiments as black-boxes and draw conclusions about the phenomenological status of their underlying structure based only on contextuality analysis of the data they generate. Secondly, regarding quantum theory, it indicates that one who accepts, as many interpretations suggest, that quantum theory satisfies both these conditions should not take for granted that quantum contextuality is a signature of non-classicality.
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.