  Recent models of carbon ignition on accreting neutron stars predict
superburst ignition depths that are an order of magnitude larger than observed.
We explore a possible solution to this problem, that the compact stars in low
mass X-ray binaries that have shown superbursts are in fact strange stars with
a crust of normal matter. We calculate the properties of superbursts on strange
stars, and the resulting constraints on the properties of strange quark matter.
We show that the observed ignition conditions exclude fast neutrino emission in
the quark core, for example by the direct Urca process, which implies that
strange quark matter at stellar densities should be in a color superconducting
state. For slow neutrino emission in the quark matter core, we find that
reproducing superburst properties requires a definite relation between three
poorly constrained properties of strange quark matter: its thermal
conductivity, its slow neutrino emissivity and the energy released by
converting a nucleon into strange quark matter.
