  We reconstruct the Lorentzian graviton propagator in asymptotically safe
quantum gravity from Euclidean data. The reconstruction is applied to both the
dynamical fluctuation graviton and the background graviton propagator. We prove
that the spectral function of the latter necessarily has negative parts similar
to, and for the same reasons, as the gluon spectral function. In turn, the
spectral function of the dynamical graviton is positive. We argue that the
latter enters cross sections and other observables in asymptotically safe
quantum gravity. Hence, its positivity may hint at the unitarity of
asymptotically safe quantum gravity.
