Conciliation of Bayes and Pointwise Quantum State Estimation: Asymptotic information bounds in quantum statistics

@article{Gill2005ConciliationOB,
  title={Conciliation of Bayes and Pointwise Quantum State Estimation: Asymptotic information bounds in quantum statistics},
  author={R. Gill},
  journal={arXiv: Statistics Theory},
  year={2005}
}
  • R. Gill
  • Published 2005
  • Mathematics, Physics
  • arXiv: Statistics Theory
  • We derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of the resulting data. The bound is an integrated version of a quantum Cram\'er-Rao bound due to Holevo (1982), and it thereby links the fixed N exact Bayesian optimality usually pursued in the physics literature with the pointwise asymptotic optimality favoured… CONTINUE READING
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    References

    SHOWING 1-10 OF 21 REFERENCES
    Asymptotics in quantum statistics
    • 21
    • PDF
    State estimation for large ensembles
    • 175
    • PDF
    Optimal full estimation of qubit mixed states
    • 71
    • PDF
    Distinguishability and Accessible Information in Quantum Theory
    • 199
    • PDF
    Asymptotic performance of optimal state estimation in quantum two level system
    • 29
    • PDF
    On Quantum Statistical Inference, II
    • 4
    • PDF
    On quantum statistical inference
    • 135
    • PDF
    Asymptotic theory of quantum statistical inference : selected papers
    • 114
    Local asymptotic normality for qubit states
    • 61
    • PDF
    Applications of the van Trees inequality : a Bayesian Cramr-Rao bound
    • 278
    • PDF