Papers › Haar-random and pretty good measurements for Bayesian state estimation
Haar-random and pretty good measurements for Bayesian state estimation
Maria Quadeer
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We study Haar-random bases and pretty good measurement for Bayesian state estimation. Given N Haar-random bases we derive a bound on fidelity averaged over IID sequences of such random measurements for a uniform ensemble of pure states. For ensembles of mixed qubit states, we find that measurements defined through unitary 2-designs closely approximate those defined via Haar random unitaries while the Pauli group only gives a weak lower bound. For a single-shot-update, we show using the Petz recovery map for pretty good measurement that it can give pretty good Bayesian mean estimates.
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