The detection of GW170817 and the identification of its host galaxy have allowed for the first standard-siren measurement of the Hubble constant, with an uncertainty of $sim 14%$. As more detections of binary neutron stars with redshift measurement are made, the uncertainty will shrink. The dominating factors will be the number of joint detections and the uncertainty on the luminosity distance of each event. Neutron star black hole mergers are also promising sources for advanced LIGO and Virgo. If the black hole spin induces precession of the orbital plane, the degeneracy between luminosity distance and the orbital inclination is broken, leading to a much better distance measurement. In addition neutron star black hole sources are observable to larger distances, owing to their higher mass. Neutron star black holes could also emit electromagnetic radiation: depending on the black hole spin and on the mass ratio, the neutron star can be tidally disrupted resulting in electromagnetic emission. We quantify the distance uncertainty for a wide range of black hole mass, spin and orientations and find that the 1-$sigma$ statistical uncertainty can be up to a factor of $sim 10$ better than for a non-spinning binary neutron star merger with the same signal-to-noise ratio. The better distance measurement, the larger gravitational-wave detectable volume, and the potentially bright electromagnetic emission, imply that spinning black hole neutron star binaries can be the optimal standard siren sources as long as their astrophysical rate is larger than $O(10)$ Gpc$^{-3}$yr$^{-1}$, a value allowed by current astrophysical constraints.
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