Qubit Quantum Metrology in the Regime of Limited Resources

It has been demonstrated that quantum resources, such as entanglement, can decrease the uncertainty of parameter estimation. A tight lower bound for this uncertainty exists for the regime of asymptotic measurement resources. Several bounds have been proposed for the more realistic non-asymptotic regime, but none are tight. We investigate the regime of non-asymptotic resources for a specific system: using nu qubit probes to estimate a rotation angle externally induced on the probes. We introduce a Bayesian modeling framework for qubit quantum metrology. We numerically investigate the effect of quantum correlations on parameter estimation uncertainty as a function of nu. We find that, even in the non-asymptotic regime, increased entanglement results in a lower uncertainty. However, the uncertainty measured by probes with intermediate amounts of entanglement exhibits more variation than either separable probes or maximally entangled probes.