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Explore the theoretical foundations of quantum sensing through a conference talk examining the breakdown of the Cramér-Rao formalism in multi-parameter quantum estimation. Investigate the physical origins of singularities in the quantum Fisher information matrix (QFIM) and discover how these singularities arise from over-parametrization at the metrological level. Learn about emergent metrological symmetries that occur when identical measurement outcomes result from different parameter combinations, causing the traditional Cramér-Rao bound framework to fail. Understand how global Bayesian estimation strategies can reveal effective parameter encoding even when conventional formalism provides limited information. Examine concrete examples demonstrating how to deduce the number of effective parameters and their encoding in singular quantum estimation scenarios. Gain insights into advanced quantum metrology concepts including multi-parameter Cramér-Rao bounds, quantum Fisher information matrices, and the relationship between system symmetries and parameter estimation precision limits.
