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arXiv:1002.3135 · Physical Review A

Proposed test of macroscopic quantum contextuality

Adán Cabello

Published Sep 13, 2010• 27 citations
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Abstract

We show that, for any system with a number of levels which can be identified with $n$ 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 $n$, and the tolerated error per correlation also increases with $n$, showing that state-independent quantum contextuality is experimentally observable in complex systems.

DOI
10.1103/physreva.82.032110

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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.
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.
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.
We propose a test of quantum contextuality for a single three-level system that uses nine projective measurements. It has the form of an inequality that has to be satisfied by any noncontextual theory. We show that for any qutrit state, except for the maximally mixed state, one can always find a set of nine observables for which the corresponding inequality is violated. This inequality is a test of contextuality that may offer insight into the relation between state-dependent and state-independent contextuality tests present in the literature.