  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 neutron
[Y. Hasegawa et al., Nature (London) 425, 45 (2003)] based on violations of
Clauser-Horne-Shimony-Holt-like inequalities.
