Efficient estimation of error bounds for quantum multiparametric imaging with constraints

Advanced superresolution imaging techniques require specific approaches for accurate and consistent estimation of the achievable spatial resolution. Fisher information supplied to the Cram\'er-Rao bound (CRB) has proved to be a powerful and efficient tool for resolution analysis and optical setups optimization. However, the standard CRB is not applicable to constrained problems violating the unbiasedness condition, while such models are frequently encountered in quantum imaging of complex objects. Complementary to the existing approaches based on modifying CRB, we propose a practical algorithm for approximate construction of a modified Fisher information matrix, which takes the constraints into account and enables accurate estimation of errors for constrained problems by the standard CRB. We demonstrate the efficiency of the proposed technique by applying it to one-, two-, and multiparameter model problems in quantum imaging. The approach provides quantitative explanation of previous results with successful experimental reconstruction of objects with the spatial scale smaller than the theoretical limit predicted by the standard CRB.

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