  We propose how to achieve nonreciprocal quantum entanglement of light and
motion and reveal its counterintuitive robustness against random losses. We
find that by splitting the counterpropagating lights of a spinning resonator
via the Sagnac effect, photons and phonons can be entangled strongly in a
chosen direction but fully uncorrelated in the other. This makes it possible
both to realize quantum nonreciprocity even in the absence of any classical
nonreciprocity and also to achieve significant entanglement revival against
backscattering losses in practical devices. Our work provides a way to protect
and engineer quantum resources by utilizing diverse nonreciprocal devices, for
building noise-tolerant quantum processors, realizing chiral networks, and
backaction-immune quantum sensors.
