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

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 a given temperature; (ii) independent identically prepared qubits with a 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 the 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 independent and identically distributed (i.i.d.) spin-(1/2) systems in an arbitrary unknown state {rho} and look for the measurement-preparation pair (M{sub n},P{sub n}) for which the reconstructed state {omega}{sub n}:=P{sub n} circle M{sub n}({rho}{sup xn}) is as close as possible to the input state (i.e., parallel {omega}{sub n}-{rho}{sup xn} parallel {sub 1} is small). The figure of merit is based on the trace norm distance between the input and output states. We show that asymptotically with n this problem is equivalent to the first one.more » The proof and construction of (M{sub n},P{sub 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 to 'optimal estimation', showing that 'benchmarking' and estimation are closely related problems in the asymptotic set up.« less

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