  A protocol for remote state preparation is proposed for spin ensembles, where
the aim is to prepare a state with a given set of spin expectation values on a
remote spin ensemble using entanglement, local spin rotations, and measurements
in the Fock basis. The spin ensembles could be realized by thermal atomic
ensembles or spinor Bose-Einstein condensates. The protocol works beyond the
Holstein-Primakoff approximation, such that spin expectation values for the
full Bloch sphere can be prepared. The main practical obstacle is the
preparation of the maximally entangled state between the spin ensembles. To
overcome this, we examine using states based on the two-axis two-spin (2A2S)
Hamiltonian in place of the maximally entangled state and examine its
performance. We find that the version of the protocol with 2A2S squeezing
well-approximates the maximally entangled state, such that spin averages can be
remotely prepared. We evaluate the errors of using 2A2S squeezed states, and
find that it decreases with the ensemble size. With post-selection, errors can
be systematically decreased further.
