.Quantum sensors based on frequentist interferometry face a trade off between sensitivity and dynamic range Bayesian quantum estimation, combining Bayesian statistics with quantum metrology, can surpass the limit of conventional frequentist measurements For cold atom CPT clocks, our adaptive Bayesian protocol achieves Heisenberg limited sensitivity in integration time and improves fractional frequency stability by 5 1 4 dB over conventional PID locking while enhancing robustness against technical noise In CPT magnetometry, we optimize measurement sequences to improve precision scaling from T 0 5 to T 0 85 Using Bayesian quantum estimation to optimize the interferometry sequence, we yield a 145 6 nT dynamic range 14 6 dB higher than frequentist counterpart of 5 0 nT) with a sensitivity of 6 8 0 1 pT/Hz¹ ² 3 3 dB improvement over the frequentist counterpart of 14 7 0 4 pT/Hz¹ ²) In addition to atomic clocks and magnetometers, this framework may bridge high sensitivity and broad dynamic range for other interferometry based quantum sensors.
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