Can communication power of separable correlations exceed that of entanglement resource?

The scenario of remote state preparation with shared correlated quantum state and one bit of forward communication [B. Dakic et al. Nature Physics 8, 666-670 (2012)] is considered. The transmission efficiency is examined by considering general encoding and decoding strategies. The importance of use of linear fidelity is recognized. It is shown that separable states cannot exceed the efficiency of entangled states in this protocol. It is proven however that such a surprising phenomena may naturally occur when the decoding agent has limited resources in the sense that either (i) has no information about the coordinates in the sender plane being in question or (ii) is forced to use bistochastic operations only which may be imposed by physically inconvenient local thermodynamical conditions.