We derive fundamental bounds for general quantum metrological models involving both temporal or spatial correlations (mathematically described by quantum combs), which may be effectively computed in the limit of a large number of probes or sensing channels involved. Although the bounds are not guaranteed to be tight in general, their tightness may be systematically increased by increasing the numerical complexity of the procedure. Interestingly, this approach yields bounds tighter than the state of the art also for uncorrelated channels. We apply the bounds to study the limits for the most general adaptive phase estimation models in the presence of temporally correlated dephasing. We consider dephasing both parallel (no Heisenberg scaling) and perpendicular (Heisenberg scaling possible) to the signal. In the former case our new bounds show that negative correlations are beneficial; for the latter we show evidence that the bounds are tight. We also apply the bounds to collisional thermometry, i.e., estimation of a parameter of the environment, showing evidence that entangled probes may provide only a limited advantage.

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• Open quantum systems & decoherence
• Quantum Fisher information
• Quantum control
• Quantum metrology
• Quantum sensing