Proposed Experiment for Testing Quantum Contextuality with Neutrons

We show that an experimental demonstration of quantum contextuality using 2 degrees of freedom of single neutrons based on a violation of an inequality derived from the Peres-Mermin proof of the Kochen-Specker theorem would be more conclusive than those obtained from previous experiments involving pairs of ions [M. A. Rowe et al., Nature (London) 409, 791 (2001)] and single neutrons [Y. Hasegawa et al., Nature (London) 425, 45 (2003)] based on violations of Clauser-Horne-Shimony-Holt-like inequalities.

Figure 1

Above: A proposed experimental setup with a neutron interferometer. The interferometer has two functions: the first half as a state generator, and the second half as a path measurement apparatus. In both parts, a phase shifter (PS) as well as a pair of spin rotators (SR) which enable relative phase and spinor manipulations are inserted. The outgoing beam suffers a spin measurement. Below: Three diagrams for the different measurements required to test the inequality (4). (i) For measurements of ${\sigma }_x^s·{\sigma }_x^p$ and ${\sigma }_y^s·{\sigma }_y^p$: After going through a state generator ($G$), a state suffers a path measurement ($P$) followed by a spin measurement ($S$). Consequently, each outgoing beam gives the results of the two measurements. (ii) For measurements of ${\sigma }_y^s{\sigma }_x^p·{\sigma }_x^s{\sigma }_y^p$: By tuning one of the spin rotators to a spin-flip operation in the path measurement part, the second half of the interferometer together with a spin analyzer ($P+S$) work as a Bell-state discriminator: four outgoing beams are assigned to the four possible results of the measurements. (iii) For measurements of ${\sigma }_y^s{\sigma }_x^p·{\sigma }_y^s·{\sigma }_x^p$ and ${\sigma }_x^s{\sigma }_y^p·{\sigma }_x^s·{\sigma }_y^p$: After the apparatus $P+S$, a state mixer ($M$) eliminates the former information about the result of either observable, and is followed by a path and a spin measurement.