Higher-order noise statistics restore Heisenberg scaling under collective dephasing

• URL: http://arxiv.org/abs/2607.02962v1
• Date: Fri, 03 Jul 2026 05:12:17 GMT
• Title: Higher-order noise statistics restore Heisenberg scaling under collective dephasing
• Abstract summary: Noisy-metrology theory characterizes decoherence by its two-point correlation function, equivalently the singleatom coherence time or noise spectrum.<n>We show this is insufficient for entangled probes: two collective baths with identical single-atom $T$ but different entanglement-enhanced scaling.<n>We prove that the Gaussian floor is the exact worst case: at fixed single-atom coherence time every finite-rate kick statistics strictly beats it, and for arbitrary Lévy phase noise the entangled-probe sensitivity is set exclusively by the diffusive component.
• Score: 7.1895670906071
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Noisy-metrology theory characterizes decoherence by its two-point correlation function, equivalently the single-atom coherence time or noise spectrum. We show this is insufficient for entangled probes: two collective baths with identical single-atom $T_2$ but different higher-order statistics yield opposite entanglement-enhanced scaling. Under Gaussian Markovian collective dephasing a Greenberger--Horne--Zeilinger (GHZ) probe reaches an atom-number-independent sensitivity floor. For a fully Markovian compound-Poisson bath, in which collective dephasing is generated by a finite-rate sequence of unitary phase kicks, a Dicke coherence of order $q$ (a difference of $J_z$ eigenvalues) decays at $Γ_q=Γ[1-\mathrm{Re}\,\varphi(q)]$, with $\varphi$ the kick characteristic function; for any absolutely continuous kick law this rate saturates at large $q$ instead of growing as $q^2$, and a GHZ probe recovers Heisenberg scaling $δω\propto1/N$ over the window in which collective finite-rate noise dominates residual independent decoherence. We prove that the Gaussian floor is the exact worst case: at fixed single-atom coherence time every finite-rate kick statistics strictly beats it, and for arbitrary Lévy phase noise the asymptotic entangled-probe sensitivity is set exclusively by the diffusive component. A converse bound shows that no input state, ancilla, or measurement improves on the GHZ scaling. The mechanism is purely exponential and CP-divisible, distinct from the Zeno, non-Markovian, nonlinear-generator, and error-correction routes. A dissipative analogue caps the Dicke superradiant burst. The full counting statistics of common noise thus emerge as a control axis for noisy quantum metrology, beyond the spectrum.

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