Kadanoff Seminar: Probing Sign Structure using Measurement-induced Entanglement. - Tim Hsieh, Perimeter

Probing Sign Structure using Measurement-induced Entanglement.

The sign structure of quantum states is closely connected to quantum phases of matter, yet detecting such fine-grained properties of amplitudes is subtle.  Here we employ as a diagnostic measurement-induced entanglement (MIE)-- the average entanglement generated between two parties after measuring the rest of the system.  We propose that for a sign-free state, the MIE upon measuring in the sign-free basis decays no slower than the slowest correlation function of the state.  Concretely, we prove that MIE is upper bounded by mutual information for sign-free stabilizer states, which establishes a bound between scaling dimensions of conformal field theories describing measurement-induced critical points in stabilizer systems.  We also verify our proposal in several critical ground states of one-dimensional systems, including the transverse field Ising, tri-critical Ising, and 3-state Potts models.  In contrast, for states with sign structure, such bounds can be violated, as we illustrate in critical hybrid circuits involving both Haar or Clifford random unitaries and measurements, and gapless symmetry-protected topological states.