Optimal asymptotic precision bounds for nonlinear quantum metrology under collective dephasing

• URL: http://arxiv.org/abs/2501.00189v1
• Date: Mon, 30 Dec 2024 23:55:24 GMT
• Title: Optimal asymptotic precision bounds for nonlinear quantum metrology under collective dephasing
• Authors: Francisco Riberi, Lorenza Viola,
• Abstract summary: Dephasing noise remains a leading source of decoherence in state-of-the-art quantum sensing platforms. We analyze the impact of classical em collective dephasing with arbitrary temporal correlations on the performance of generalized interferometry protocols.
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• Abstract: Interactions among sensors can provide, in addition to entanglement, an important resource for boosting the precision in quantum estimation protocols. Dephasing noise, however, remains a leading source of decoherence in state-of-the-art quantum sensing platforms. We analyze the impact of classical {\em collective dephasing with arbitrary temporal correlations} on the performance of generalized Ramsey interferometry protocols with \emph{quadratic} encoding of a target frequency parameter. The optimal asymptotic precision bounds are derived for both product coherent spin states and for a class of experimentally relevant entangled spin-squeezed states of $N$ qubit sensors. While, as in linear metrology, entanglement offers no advantage if the noise is Markovian, a precision scaling of $N^{-1}$ is reachable with classical input states in the quadratic setting, which is improved to $N^{-5/4}$ when temporal correlations are present and the Zeno regime is accessible. The use of nonclassical spin-squeezed states and a nonlinear readout further allows for an $N^{-3/2}$ precision scaling, which we prove is asymptotically optimal. We also show how to counter {\em noise-induced bias} by introducing a simple ratio estimator which relies on detecting two suitable system observables, and show that it remains asymptotically unbiased in the presence of dephasing, without detriment to the achievable precision.

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