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Physical Review A

Quantum contextuality in a one-dimensional quantum harmonic oscillator

Hong-Yi Su, Jing‐Ling Chen, Chunfeng Wu, Sixia Yu, C. H. Oh

Published May 29, 2012• 10 citations
Publisher

Abstract

We investigate quantum contextuality of one-dimensional quantum harmonic oscillator. Through the violation of a noncontextuality inequality, any eigenstate of quantum harmonic oscillator and some typical continuous-variable states, such as the coherent state and the squeezed state, exhibit quantum contextuality. The state-independent demonstration of quantum contextuality in continuous-variable states is also demonstrated.

DOI
10.1103/physreva.85.052126

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We investigate quantum contextuality of one-dimensional quantum harmonic oscillator. Through the violation of a noncontextuality inequality, any eigenstate of quantum harmonic oscillator and some typical continuous-variable states, such as the coherent state and the squeezed state, exhibit quantum contextuality. The state-independent demonstration of quantum contextuality in continuous-variable states is also demonstrated.
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.
Physical potentials are routinely approximated to harmonic potentials. Hence it is important to know when a quantum harmonic oscillator (QHO) behaves quantum mechanically and when classically. Recently Su et al. ( Phys. Rev. A , 85 (2012) 052126) have theoretically shown that QHO exhibits quantum contextuality (QC) for a certain set of pseudospin observables. Here we encode the four eigenstates of a QHO onto four Zeeman product states of a pair of spin-(1/2) nuclei. Using the techniques of NMR quantum information processing, we then demonstrate the violation of both state-dependent and state-independent inequalities arising from the noncontextual hidden variable model.
We investigate the violation of noncontextuality by a class of continuous-variable states, including variations of entangled coherent states and a two-mode continuous superposition of coherent states. We generalize the Kochen-Specker (KS) inequality discussed by Cabello [A. Cabello, Phys. Rev. Lett. 101, 210401 (2008)] by using effective bidimensional observables implemented through physical operations acting on continuous-variable states, in a way similar to an approach to the falsification of Bell-Clauser-Horne-Shimony-Holt inequalities put forward recently. We test for state-independent violation of KS inequalities under variable degrees of state entanglement and mixedness. We then demonstrate theoretically the violation of a KS inequality for any two-mode state by using pseudospin observables and a generalized quasiprobability function.
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.