Butterfly echo protocol for axis-agnostic Heisenberg-limited metrology

Highly entangled many-body states are valuable resources for quantum-enhanced precision metrology. Whereas the canonical example -- the GHZ state -- facilitates Heisenberg-limited sensing of Bloch-sphere rotations about a particular known and fixed axis, recent work has explored the use of axis-agnostic probe states that are sensitive to 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. practical algorithms for efficiently generating these axis-agnostic probe states using random circuit dynamics and 2. an experimentally feasible `butterfly echo' protocol for utilizing these probe states based on the principle of quantum information scrambling. More generally, the technical methods I discuss here allow for analytically tractable models for studying the interplay of scrambling, decoherence, and weak measurements in near-term all-to-all experimental platforms including cavity QED and trapped ions.