  Optomechanical quantum interfaces can be utilized to connect systems with
distinctively different frequencies in hybrid quantum networks. Here we present
a scheme of nonreciprocal quantum state conversion between microwave and
optical photons via an optomechanical interface. By introducing an auxiliary
cavity and manipulating the phase differences between the linearized
optomechanical couplings, uni-directional state transmission can be achieved.
The interface can function as an isolator, a circulator, and a two-way switch
that routes the input states to a selected output channel. We show that under a
generalized impedance matching condition, the state conversion can reach high
fidelity and is robust against the thermal fluctuations in the mechanical mode.
