  We construct an observable mixed state topological order parameter for
symmetry-protected free fermion matter. It resolves the entire table of
topological insulators and superconductors, relying exclusively on the symmetry
class, but not on unitary symmetries. It provides a robust, quantized signal
not only for pure ground states, but also for mixed states in- or out of
thermal equilibrium. Key ingredient is a unitary probe operator, whose phase
can be related to spectral asymmetry, in turn revealing the topological
properties of the underlying state. This is demonstrated analytically in the
continuum limit, and validated numerically on the lattice. The order parameter
is experimentally accessible via either interferometry or full counting
statistics, for example, in cold atom experiments.
