Mitigating sloppiness with intermediate controls in sequential multiparameter spin interferometry

Abstract

Multiparameter quantum sensing requires different parameters to produce distinguishable probe responses while allowing their information to be extracted simultaneously. In sequential sensing without intermediate control, two phases encoded through the same generator are locally indistinguishable. Here we show that parameter-independent intermediate controls overcome this limitation in a collective-spin interferometer by separating the corresponding effective generators in the probe covariance geometry. Specifically, a transverse collective rotation provides an analytically tractable realization, and intermediate one-axis twisting (OAT) generates additional nonlinear operator directions and a broad regime of enhanced joint estimation. For fixed total particle number $N$ and matched twisting resource, both marginal precision bounds lie below those of a separated-OAT strategy while measurement incompatibility remains weak. For intermediate OAT, conditional optimization of an upper bound on the Holevo cost yields asymptotic $N^{-2}$ scaling. For this protocol, a fixed rotated-Dicke measurement retains simultaneous two-parameter enhancement over a broad phase region. These results show that nonlinear intermediate control can mitigate sloppiness while preserving quantum-enhanced precision with a common readout.