Butterfly echo protocol for axis-agnostic Heisenberg-limited metrology

Highly entangled many-body states of matter are a valuable resource for quantum-enhanced precision metrology. Whereas the canonical example -- the GHZ state -- facilitates Heisenberg-limited measurement of Bloch-sphere rotations about a particular known and fixed axis, more recent work has explored the use of "anti-coherent" states that are sensitive to Bloch-sphere rotations about arbitrary, a priori unknown axes at sensitivities differing from the Heisenberg limit by only a factor of 3. In this talk I will present two complementary results: 1. an experimentally feasible `butterfly echo' protocol for preparing and measuring these anti-coherent states based on the principle of quantum information scrambling; and 2. analytically tractable methods for modeling the interplay of scrambling, decoherence, and weak measurement in near-term all-to-all experimental platforms including cavity QED and trapped ions.