Experimental Test of Quantum Contextuality in Neutron Interferometry

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)], a Bell-like state was generated, and three expectation values were determined. The observed violation $2.291\pm 0.008\nleqq 1$ clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden-variable theories.

Figure 1

Experimental setup: The maximally entangled Bell state $|\Psi ⟩$ is generated in the first half of a skew-symmetric interferometer. The second half of the interferometer together with a phase shifter serves as a path measurement apparatus. A spin-analysis system in the O beam allows for the selection of neutrons with certain spin properties. The spin flipper in path $|\mathrm{II}⟩$ is required for the measurement of the product observable $⟨{\sigma }_x^s{\sigma }_y^p·{\sigma }_y^s{\sigma }_x^p⟩$.

Figure 2

Typical intensity modulations obtained by varying the phase $\chi$ for the path subspace. The contrast of the sinusoidal oscillations is above 67%. The parameter $\alpha$ represents the direction of the spin analysis. In particular, the settings $\alpha =0$, $\pi$ [$\alpha =\frac{\pi }{2}$, $\frac{3\pi }{2}$] were used for measuring ${\sigma }_x^s$ [${\sigma }_y^s$]. The expectation values, $E(0,0)$ [$E(\frac{\pi }{2},\frac{\pi }{2})$], are determined from the intensities on the dashed lines, $\chi =0$, $\pi$ [$\chi =\frac{\pi }{2}$, $\frac{3\pi }{2}$].

Figure 3

Typical intensity modulations obtained by varying the phase $\chi$ in the path subspace. The two curves were recorded with opposite settings of the spin-analysis system selecting $\mid \downarrow ⟩$- and $\mid \uparrow ⟩$- components, respectively. Intensities on the dashed lines ($\chi =\frac{\pi }{2}$, $\frac{3\pi }{2}$) are used for the evaluation of the expectation value $⟨{\sigma }_x^s{\sigma }_y^p·{\sigma }_y^s{\sigma }_x^p⟩$.