  Quantum gravity models predict a minimal measurable length which gives rise
to a modification in the uncertainty principle. One of the simplest
manifestations of these generalised uncertainty principles is the linear
quadratic generalised uncertainty principle which leads to a modified
Heisenberg algebra. This can alter the usual von-Neumann evolution of density
matrix to a Lindblad-type equation. We show how this can give rise to a
decoherence in neutrino propagation in vacuum. The decoherence effects due to
the linear quadratic generalised uncertainty principle are extremely minimal
and is unlikely to be detectable in the existing or upcoming experimental
facilities for any of the natural sources of neutrinos. We also show that, in
principle, there can be other variants of generalised uncertainty principle
which predicts verifiable decoherence effects for the cosmic neutrino
background.
