  In a July 2014 Nature Communications paper, Denkmayr et al. claim to have
instantiated the so-called quantum Cheshire Cat experiment using neutron
interferometry. Crucial to this claim are the weak values which must imply the
quantum Cheshire Cat interpretation, i.e., "the neutron and its spin are
spatially separated" in their experiment. While they measured the correct weak
values for the quantum Cheshire Cat interpretation, the corresponding
implications do not obtain because, as we show, those weak values were measured
with both a quadratic and a linear magnetic field Bz interaction. We show
explicitly how those weak values imply quantum Cheshire Cat if the Bz
interaction is linear and then we show how the quadratic Bz interaction
destroys the quantum Cheshire Cat implications of those weak values. Since both
linear and quadratic Bz interactions contribute equally to the neutron
intensity in this experiment, the deviant weak value implications are
unavoidable. Because weak values were used successfully to compute neutron
intensities for weak Bz in this experiment, it is clearly the case that one
cannot make ontological inferences from weak values without taking into account
the corresponding interaction strength.
