Bayesian monotone metrics extend Petz metrics to prior-averaged states, yielding computable lower bounds on multiparameter Bayes risk that dominate van Trees bounds and can be optimized via a one-parameter subfamily.
If{K α}satisfies P α K † αKα =Iand eachX α >0, then f X α K † αXαKα ! ≥ X α K † αf(X α)Kα
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Bayesian Monotone Metrics for Multiparameter Quantum Estimation
Bayesian monotone metrics extend Petz metrics to prior-averaged states, yielding computable lower bounds on multiparameter Bayes risk that dominate van Trees bounds and can be optimized via a one-parameter subfamily.