Fig. 2: Numerical simulations of Bayesian adaptive protocols.
From: Experimental adaptive Bayesian estimation of multiple phases with limited data
For Nph = 100 pair of phases, we simulated the performance of the different strategies described in the main text, by averaging for each phase over \({N}_{\exp }=100\) different runs and by performing spline interpolation on the obtained curves. Top: quadratic loss \(L({\boldsymbol{\phi} },\hat{{\boldsymbol{\phi} }})\) (solid lines). Bottom: utility function \({\mathcal{U}}(\hat{{\boldsymbol{\phi} }})={\rm{Tr}}[{\rm{Cov}}(\hat{{\boldsymbol{\phi} }})]\) (dashed lines), corresponding to the sum of the parameters confidence intervals. Inset: (top) ratio R between the performances of each protocol, compared with the optimized strategy (ii). R is computed both for \(L({\boldsymbol{\phi }},\hat{{\boldsymbol{\phi }}})\) (solid lines) and \({\mathcal{U}}(\hat{{\boldsymbol{\phi }}})\) (dashed lines), referring the same colors of the main panels. (bottom) two-dimensional map of uniform-distributed couples of phases drawn for the simulations. Green lines: approach (i) based on the Fisher information matrix. Red lines: approach (i'), which includes first N = 20 events with random control parameters, while for N > 20 works as (i). Blue lines: optimized approach (ii). Gray lines: benchmark approach with random control parameters (iii). Dotted black lines: Cramer-Rao bound for the asymptotic regime.
