Near-deterministic weak-value metrology via collective non-linearity

Abstract Weak-value amplification employs postselection to enhance the measurement of small parameters interest. The comes at expense reduced success probability, hindering utility this technique as a tool for practical metrology. Following other quantum technologies that display advantage, we formalize advantage in probability and present scheme based on non-linear collective Hamiltonians shows super-extensive growth while simultaneously displaying an extensive weak value. We propose experimental implementation our scheme.