  Transmission efficiency (TE) of remote state preparation (RSP) with a shared
quantum state and one bit of classical communication is considered. Following
[B. Daki et al., Nat. Phys. 8, 666 (2012)], the encoding and decoding
strategies of the protocol are restricted to the physically relevant classes of
projective measurements and unitary operators, respectively. It is shown that
contrary to the previous arguments, the quadratic fidelity as well as the
linear fidelity could be a valid figure of merit to quantify the TE of RSP.
Then, the TE of the protocol in terms of both linear and quadratic fidelities
is evaluated in a fully optimized scenario which includes the maximization over
the encoding parameters as well as a meaningful maximization over the decoding
parameters. The results show that in this scenario, the TE scales with the sum
of the two largest eigenvalues of the squared correlation matrix of the
resource state that is zero only for product states. This approach successfully
quantifies the performance of the protocol in terms of the resource state
parameters and provides a means to compare the usefulness of any two resource
states for RSP.
