  A proposal to detect the purported canted antiferromagnet order for the
$\nu=0$ quantum Hall state of graphene based on a two-terminal spin transport
setup is theoretically discussed. In the presence of a magnetic field normal to
the graphene plane, a dynamic and inhomogeneous texture of the N\'eel vector
lying within the plane should mediate (nearly dissipationless) superfluid
transport of spin angular momentum polarized along the $z$ axis, which could
serve as a strong support for the canted antiferromagnet scenario. Spin
injection and detection can be achieved by coupling two spin-polarized edge
channels of the $|\nu|=2$ quantum Hall state on two opposite ends of the
$\nu=0$ region. A simple kinetic theory and Onsager reciprocity are invoked to
model the spin injection and detection processes, and the transport of spin
through the antiferromagnet is accounted for using the Landau-Lifshitz-Gilbert
phenomenology.
