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, Nature (London) 409, 791 (2001)10.1038/35057215] and single neutrons [Y. Hasegawa, Nature (London) 425, 45 (2003)10.1038/nature01881] based on violations of Clauser-Horne-Shimony-Holt-like inequalities.