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ALT Schematic of parameter estimation in two parts. Top: a compact statistical model for a quantum parameter estimation protocol. A probe state is independently transformed by the same effective parameter-dependent channel and measured over M repetitions. The resulting M measurement outcomes are then collectively processed to construct an estimator of the parameter. The bottom constructs the effective channel Eθ. The effective channel is realized by inserting multiple uses of the elementary parameter-dependent channel Nθ into the slots of a θ-independent strategy specified by the quantum operations Ci. The double dashed line denotes the ancillary system.