NMR investigation of contextuality in a quantum harmonic oscillator via pseudospin mapping

Abstract

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.