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arXiv:0912.0485 · Physical Review Letters

Testing Contextuality on Quantum Ensembles with One Clean Qubit

Osama Moussa, Colm A. Ryan, David G. Cory, Raymond Laflamme

Published Apr 23, 2010• 176 citations
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Abstract

We present a protocol to evaluate the expectation value of the correlations of measurement outcomes for ensembles of quantum systems, and use it to experimentally demonstrate--under an assumption of fair sampling--the violation of an inequality that is satisfied by any noncontextual hidden-variables theory. The experiment is performed on an ensemble of molecular nuclear spins in the solid state, using established nuclear magnetic resonance techniques for quantum-information processing.

DOI
10.1103/physrevlett.104.160501

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We present a protocol to evaluate the expectation value of the correlations of measurement outcomes for ensembles of quantum systems, and use it to experimentally demonstrate--under an assumption of fair sampling--the violation of an inequality that is satisfied by any noncontextual hidden-variables theory. The experiment is performed on an ensemble of molecular nuclear spins in the solid state, using established nuclear magnetic resonance techniques for quantum-information processing.
Often physical potentials are approximated to a harmonic potential so as to analytically solve the system dynamics. For example, the quantized electromagnetic field used to manipulate a qubit in cavity quantum electrodynamics, can be described using quantum harmonic oscillator (QHO). Hence it is important to know when a QHO behaves quantum mechanically and when classically. In this work, we encode the four lower-most eigenstates of the one dimensional-QHO(1D-QHO) onto the four Zeeman product states of a pair of spin-1/2 nuclei. Using the techniques of nuclear magnetic resonance (NMR) quantum information processing (QIP), we then demonstrate the strong violation of noncontextual hidden variable (NCHV) inequality, under specific experimental arrangements. We also experimentally investigate the weak violation of NCHV inequality by thermal equilibrium states in nuclear spins, thereby assessing their quantumness.
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.
In a noncontextual hidden variable model of quantum theory, hidden variables determine the outcomes of every measurement in a manner that is independent of how the measurement is implemented. Using a generalization of this notion to arbitrary operational theories and to preparation procedures, we demonstrate that a particular two-party information-processing task, "parity-oblivious multiplexing," is powered by contextuality in the sense that there is a limit to how well any theory described by a noncontextual hidden variable model can perform. This bound constitutes a "noncontextuality inequality" that is violated by quantum theory. We report an experimental violation of this inequality in good agreement with the quantum predictions. The experimental results also provide the first demonstration of 2-to-1 and 3-to-1 quantum random access codes.
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of classicality, the Bell theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS) . Tests of the Bell inequality and the BKS theorem are both of fundamental interests and of great significance . The Bell theorem has already been experimentally verified extensively on many different systems , while the quantum contextuality, which is independent of nonlocality and manifests itself even in a single object, is experimentally more demanding. Moreover, the contextuality has been shown to play a critical role to supply the `magic' for quantum computation, making more extensive experimental verifications in potential systems for quantum computing even more stringent. Here we report an experimental verification of quantum contextuality on an individual atomic nuclear spin-1 system in solids under ambient condition. Such a three-level system is indivisible and thus the compatibility loophole, which exists in the experiments performed on bipartite systems, is closed. Our experimental results confirm that the quantum contextuality cannot be explained by nonlocal entanglement, revealing the fundamental quantumness other than locality/nonlocality within the intrinsic spin freedom of a concrete natural atomic solid-state system at room temperature.
We performed an experimental test of the Kochen-Specker theorem based on an inequality derived from the Peres-Mermin proof, using spin-path (momentum) entanglement in a single neutron system. Following the strategy proposed by Cabello et al. [Phys. Rev. Lett. 100, 130404 (2008)10.1103/PhysRevLett.100.130404], a Bell-like state was generated, and three expectation values were determined. The observed violation 2.291 +/- 0.008 not less, dbl equals1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden-variable theories.