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arXiv:0809.0430 · Physical Review Letters

Universality of State-Independent Violation of Correlation Inequalities for Noncontextual Theories

Piotr Badziąg, Ingemar Bengtsson, Adán Cabello, Itamar Pitowsky

Published Jul 28, 2009• 110 citations
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Abstract

We show that the state-independent violation of inequalities for noncontextual hidden variable theories introduced in [Phys. Rev. Lett. 101, 210401 (2008)] is universal, i.e., occurs for any quantum mechanical system in which noncontextuality is meaningful. We describe a method to obtain state-independent violations for any system of dimension d> or =3. This universality proves that, according to quantum mechanics, there are no "classical" states.

DOI
10.1103/physrevlett.103.050401

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We show that the state-independent violation of inequalities for noncontextual hidden variable theories introduced in [Phys. Rev. Lett. 101, 210401 (2008)] is universal, i.e., occurs for any quantum mechanical system in which noncontextuality is meaningful. We describe a method to obtain state-independent violations for any system of dimension d> or =3. This universality proves that, according to quantum mechanics, there are no "classical" states.
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The quest for fundamental tests of quantum mechanics is an ongoing effort. We here address the question of what are the lowest possible moments needed to prove quantum nonlocality and noncontextuality without any further assumptions---in particular, without the often assumed dichotomy. We first show that second-order correlations can always be explained by a classical noncontextual local-hidden-variable theory. Similar third-order correlations also cannot violate classical inequalities in general, except for a special state-dependent noncontextuality. However, we show that fourth-order correlations can violate locality and state-independent noncontextuality. Finally we obtain a fourth-order continuous-variable Bell inequality for position and momentum, which can be violated and might be useful in Bell tests, closing all loopholes simultaneously.
We present an experimental state-independent violation of an inequality for noncontextual theories on single particles. We show that 20 different single-photon states violate an inequality which involves correlations between results of sequential compatible measurements by at least 419 standard deviations. Our results show that, for any physical system, even for a single system, and independent of its state, there is a universal set of tests whose results do not admit a noncontextual interpretation. This sheds new light on the role of quantum mechanics in quantum information processing.
Contextuality is an intriguing feature of quantum theory that excludes any noncontextual hidden variable theory of our nature. It is therefore a natural and important pursuit to detect as larger contextuality as possible. In the scenario to reveal contextuality through violation of noncontextuality inequality, the pursuit is to construct such inequality with large violations. In this paper, we present a simple method to extend arbitrary state-(in)dependent noncontextuality inequalities into ones with larger violations. By recursively applying the method, one can obtain noncontextuality inequalities with an arbitrary large violation. Moreover, the method also constructs quantum measurements and states to violate the new inequality.