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arXiv:2511.07211 · Quantum

Optimal phase estimation in the presence of correlated dephasing

Srijon Ghosh, Arkadiusz Kobus, Stanisław Kurdziałek, Rafał Demkowicz-Dobrzański

quant-phSubmitted Nov 10, 2025• Announced Nov 11, 2025• 0 citations
v1 · Nov 10, 2025v2 · Oct 21, 2026v3 · Oct 23, 2026v4 · Oct 28, 2026
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Abstract

We investigate optimal metrological protocols for phase estimation in the presence of correlated dephasing noise, including spin-squeezed states sensing strategies as well as parallel and adaptive protocols optimized using tensor-network based numerical methods. The results are benchmarked against fundamental bounds obtained either via a latest quantum comb extension method or an optimized classical simulation method. We find that the spin-squeezed offer practically optimal performance in the regime where phase fluctuations are positively correlated, but can be outperformed by tensor-network optimized strategies for negatively correlated fluctuations.

Journal reference
Quantum 10, 2251 (2026)
DOI
10.22331/q-2026-10-28-2251
Comments
12 pages, 5 figures

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Abstract We develop an efficient algorithm for determining optimal adaptive quantum estimation protocols with arbitrary quantum control operations between subsequent uses of a probed channel.We introduce a tensor network representation of an estimation strategy, which drastically reduces the time and memory consumption of the algorithm, and allows us to analyze metrological protocols involving up to N = 50 qubit channel uses, whereas the state-of-the-art approaches are limited to N < 5. The method is applied to study the performance of the optimal adaptive metrological protocols in presence of various noise types, including correlated noise.
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 collective dephasing with arbitrary temporal correlations on the performance of generalized Ramsey interferometry protocols with quadratic encoding of a target frequency parameter. The optimal asymptotic precision bounds are derived for both product coherent spin states and 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 noise-induced bias by introducing a simple ratio estimator, which relies on detecting two suitable system observables, and we show that it remains asymptotically unbiased in the presence of dephasing, without detriment to the achievable precision.
We show an explicit NNN-qubit protocol involving one-axis-twisted spin squeezed states, that allows for simultaneous phase and dephasing strength estimation with precision that asymptotically matches fundamental quantum metrological bounds. The relevance of the protocol goes beyond this particular model, since any uncorrelated noise quantum metrological model, that allows for at most constant asymptotic quantum enhancement, can be reduced to this problem via an appropriately tailored quantum error-correction procedure.
We study a phase estimation protocol based on the distribution of a single squeezed state among an array of Mach-Zehnder interferometers (MZIs). The fundamental component of our scheme is the quantum circuit (QC), a linear network that optimally distributes the squeezing generated at one of its inputs among the d MZIs, where d unknown parameters θ1, . . . , θd are then imprinted and the number of photons at the outputs finally measured. For any given linear combination of the parameters, we can optimize the QC and achieve sub-shot-noise sensitivity. Our parallel strategy, based on the mode-entanglement created by the QC, outperforms the rival and more common sequential strategy, in which the same unknown parameters are estimated independently. It also saturates the ultimate sensitivity bound, the quantum Cramer-Rao bound, in a relevant regime of parameters, thus constituting an optimal estimation method in that regime.
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