Precision scaling under spatially correlated and non-Markovian dephasing
In plain words
Real noise often hits all atoms together or has memory in time. How the best achievable precision then scales with particle number and time is known only in special cases.
Precise statement
For $N$ qubits sensing a phase under dephasing with spatial correlation function $C(r)$ and temporal spectrum $S(\omega)$, including the non-Markovian Zeno regime, classify the asymptotic scaling exponent of the minimal estimation error with $N$ and total time $T$, and identify the states and measurements attaining it.
What would settle it
Bounds and attaining protocols covering the main classes of correlated noise, with matching exponents.
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