  We show how to communicate Heisenberg-limited continuous (quantum) variables
between Alice and Bob in the case where they occupy two inertial reference
frames that differ by an unknown Lorentz boost. There are two effects that need
to be overcome: the Doppler shift and the absence of synchronized clocks.
Furthermore, we show how Alice and Bob can share Doppler-invariant
entanglement, and we demonstrate that the protocol is robust under photon loss.
