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A successful state transfer (or teleportation) experiment must perform betterthan the benchmark set by the `best' measure and prepare procedure. We considerthe benchmark problem for the following families of states: (i) displacedthermal equilibrium states of given temperature; (ii) independent identicallyprepared qubits with completely unknown state. For the first family we showthat the optimal procedure is heterodyne measurement followed by thepreparation of a coherent state. This procedure was known to be optimal forcoherent states and for squeezed states with the `overlap fidelity' as figureof merit. Here we prove its optimality with respect to the trace norm distanceand supremum risk. For the second problem we consider n i.i.d. spin-1/2 systemsin an arbitrary unknown state $\rho$ and look for the measurement-preparationpair $(M_{n},P_{n})$ for which the reconstructed state $\omega_{n}:=P_{n}\circM_{n} (\rho^{\otimes n})$ is as close as possible to the input state, i.e.$\|\omega_{n}- \rho^{\otimes n}\|_{1}$ is small. The figure of merit is basedon the trace norm distance between input and output states. We show thatasymptotically with $n$ the this problem is equivalent to the first one. Theproof and construction of $(M_{n},P_{n})$ uses the theory of local asymptoticnormality developed for state estimation which shows that i.i.d. quantum modelscan be approximated in a strong sense by quantum Gaussian models. Themeasurement part is identical with `optimal estimation', showing that`benchmarking' and estimation are closely related problems in the asymptoticset-up.

Quantum teleportation benchmarks for independent and identically-distributed spin states and displaced thermal states