In the dilute limit of a Brownian all-to-all circuit, the renormalized OTOC grows at the unperturbed chaos rate at early times and saturates to a value set by r/(1+kappa), showing no localization phase transition.
Approaching the Heisenberg limit without single-particle detection
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abstract
We propose an approach to quantum phase estimation that can attain precision near the Heisenberg limit without requiring single-particle-resolved state detection. We show that the "one-axis twisting" interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Applying this interaction-based readout to oversqueezed, non-Gaussian states yields a Heisenberg scaling in phase sensitivity, which persists in the presence of detection noise as large as the quantum projection noise of an unentangled ensemble. Even in dissipative implementations -- e.g., employing light-mediated interactions in an optical cavity or Rydberg dressing -- the method significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit.
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Scrambling Dynamics with Imperfections in a Solvable Model
In the dilute limit of a Brownian all-to-all circuit, the renormalized OTOC grows at the unperturbed chaos rate at early times and saturates to a value set by r/(1+kappa), showing no localization phase transition.