. The reported Qlosses refer to the average of over 100 triplets of phases of the median Qloss computed over 30 repetitions of the estimation protocol of different experiments. For the sake of demonstrating the goodness of the experimental results, we perform some simulations using the lHd function of the real device reconstructed from experimental grids knowing the model of the system .
We can implement such automated protocol thanks to the use of a programmable integrated photonic circuit, which allows us to control the performed measurements, easily configuring control parameters to implement adaptive protocols in a fully black-box fashion using quantum states. The implementation of a model-free approach for quantum multiparameter estimation paves the way for everyday automated use of complex quantum sensors without the need of time- and resource-consuming characterization or the requirement of a faithful theoretical modeling. The latter can be a fundamental limitation in all the scenarios where the theoretical description of the whole quantum evolution is lacking.
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