Efficient estimation of error bounds for quantum multiparametric imaging with constraints

Abstract: Advanced super-resolution imaging techniques require specific approaches for accurate and consistent estimation of the achievable spatial resolution. Fisher information supplied to Cramer-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. Complimentary 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 can be supplied to the standard CRB. We demonstrate the efficiency of the proposed technique by applying it to 1-, 2-, and multi-parameter 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.