Brownian spin dynamics for axis-agnostic precision metrology

Anticoherent states are known to enable Heisenberg-limited precision measurements of external fields B→ = Bnˆ along arbitrary, apriori unknown rotation axes ˆn. In this paper we propose efficient protocols for producing approximate anticoherent states using random circuit dynamics acting on a single large spin S→. In particular, we propose two circuit models (Brownian and Random One-Axis Twist) to efficiently generate anticoherent spin states. Using the Choi-Jamio lkowski isomorphism (channel-state duality), we demonstrate that the behavior of these two models is identical given sufficiently short twisting times, and that these models can reach approximate anticoherence in constant circuit depth in the large-S limit.