  A successful state transfer (or teleportation) experiment must perform better
than the benchmark set by the `best' measure and prepare procedure. We consider
the benchmark problem for the following families of states: (i) displaced
thermal equilibrium states of given temperature; (ii) independent identically
prepared qubits with completely unknown state. For the first family we show
that the optimal procedure is heterodyne measurement followed by the
preparation of a coherent state. This procedure was known to be optimal for
coherent states and for squeezed states with the `overlap fidelity' as figure
of merit. Here we prove its optimality with respect to the trace norm distance
and supremum risk. For the second problem we consider n i.i.d. spin-1/2 systems
in an arbitrary unknown state $\rho$ and look for the measurement-preparation
pair $(M_{n},P_{n})$ for which the reconstructed state $\omega_{n}:=P_{n}\circ
M_{n} (\rho^{\otimes n})$ is as close as possible to the input state, i.e.
$\|\omega_{n}- \rho^{\otimes n}\|_{1}$ is small. The figure of merit is based
on the trace norm distance between input and output states. We show that
asymptotically with $n$ the this problem is equivalent to the first one. The
proof and construction of $(M_{n},P_{n})$ uses the theory of local asymptotic
normality developed for state estimation which shows that i.i.d. quantum models
can be approximated in a strong sense by quantum Gaussian models. The
measurement part is identical with `optimal estimation', showing that
`benchmarking' and estimation are closely related problems in the asymptotic
set-up.
