Optimal Extraction of Information from Finite Quantum Ensembles

Abstract

Given only a finite ensemble of identically prepared particles, how precisely can one determine their states'? We describe optimal measurement procedures in the case of spin 1/2 particles. Furthermore, we prove that optimal measurement procedures must necessarily view the ensemble as a single composite system rather than as the sum of its components, i.e. , optimal measurements cannot be realized by separate measurements on each particle.

Ground-to-satellite quantum teleportation

“…To optimize the link efficiency and overcome the atmospheric turbulence in the up-link, a series of techniques are developed, including a compact ultra-bright source of multi-photon entanglement, narrow beam divergence, high-bandwidth and high-accuracy acquiring, pointing, and tracking (APT). We demonstrate successful quantum teleportation for six input states in mutually unbiased bases with an average fidelity of 0.80±0.01, well above the classical limit 14 . This work establishes the first ground-to-satellite up-link for faithful and ultra-long-distance quantum teleportation, an essential step toward global-scale quantum internet.…”

Local Asymptotic Normality in Quantum Statistics

“…Asymptotic inference is now a well established topic in quantum statistics, with many papers [32,8,52,12,26,3,20,19,4,11] concentrating on the problem of estimating an unknown state ρ using the results of measurements performed on n quantum systems, identically prepared in the state ρ. For two dimensional systems, or qubits, the optimal state estimation problem has an explicit solution [4] in the special context of Bayesian inference, with invariant priors and figure of merit (risk) based on the fidelity distance between states.…”

Game-theoretic discussion of quantum state estimation and cloning

“…We also note that the quantum state estimation and quantum cloning games that we consider here, are equivalent to the games discussed in Ref. [7] and Ref. [8] respectively.…”