Echoed Random Quantum Metrology

Abstract: Quantum metrology typically demands the preparation of exotic quantum probe states, such as entangled or squeezed states, to surpass classical limits. However, the need for carefully calibrated system parameters and finely optimized quantum controls imposes limitations on scalability and robustness. Here, we circumvent these limitations by introducing an echoed random process that achieves sensitivity approaching the Heisenberg limit while remaining blind to the random probe state. We demonstrate that by simply driving a Kerr nonlinear mode with random pulses, the emergence of sub-Planck phase-space structures grants high sensitivity, eliminating the need for complex quantum control. The protocol is statistically robust, yielding high performance across broad driving parameter ranges while exhibiting resilience to control fluctuations and photon loss. Broadly applicable to both bosonic and qubit platforms, our work reveals a practical, hardware-efficient, scalable, and optimization-free route to quantum-enhanced metrology in high-dimensional Hilbert spaces.