Remote state preparation of two-component Bose-Einstein condensates

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 the protocol 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 that are introduced by using 2A2S squeezed states, and find that it decreases with the ensemble size. With postselection, errors can be systematically decreased further.