Entanglement Enhanced Sensing with Qubits affected by non-Markovian Dephasing

Anders S{\o}ndberg S{\o}rensen; Anders S. S{\o}rensen; Kasper Hede Nielsen; Noah Kaufmann

arxiv: 2604.22368 · v2 · submitted 2026-04-24 · 🪐 quant-ph

Entanglement Enhanced Sensing with Qubits affected by non-Markovian Dephasing

Noah Kaufmann , Kasper Hede Nielsen , Anders S{\o}ndberg S{\o}rensen , Anders S. S{\o}rensen This is my paper

Pith reviewed 2026-05-08 11:57 UTC · model grok-4.3

classification 🪐 quant-ph

keywords entanglementquantum sensingRamsey spectroscopydephasing noisecorrelated noisenon-Markovian noisequantum metrology

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The pith

Entangled probes achieve better sensitivity scaling than separable states under correlated dephasing noise.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that entanglement can still deliver a quantum advantage in sensing weak signals even when qubits experience dephasing noise, but only when that noise correlates across successive experimental shots. It derives a basic bound: sensitivity cannot exceed the signal-to-noise ratio that the probe itself experiences. Under suitable spatial and temporal correlations in the noise, entangled states of multiple qubits then produce a more favorable scaling of precision with probe number than independent separable states. The result applies to Ramsey spectroscopy with pure classical dephasing and demonstrates that realistic correlated noise does not necessarily erase the benefit of entanglement.

Core claim

For suitable spatial and temporal correlations in the noise, entangled probes achieve a better scaling of the sensitivity with the number of probes than separable states. This follows from a simple fundamental limit: the sensitivity cannot be better than the signal-to-noise ratio seen by the probe. The demonstration is specific to Ramsey spectroscopy with probes subject to pure classical dephasing.

What carries the argument

A fundamental sensitivity bound set by the signal-to-noise ratio experienced by the probe, applied to compare scaling for entangled versus separable states under correlated classical dephasing.

If this is right

Entanglement improves the scaling of sensitivity with probe number when noise correlations span multiple measurements.
The quantum advantage survives in non-Markovian dephasing provided the correlations are suitable in space and time.
The result applies directly to Ramsey spectroscopy using qubits subject to pure classical dephasing.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same noise-correlation strategy could be tested in other metrology protocols such as phase estimation or magnetometry.
Experimental designs might deliberately engineer or select for temporal correlations to recover entanglement gains in noisy environments.
The bound based on probe signal-to-noise ratio offers a general tool for assessing quantum advantage in any sensing task with repeated measurements.

Load-bearing premise

The dephasing noise must exhibit correlations across multiple successive shots, and sensitivity cannot exceed the signal-to-noise ratio experienced directly by the probes.

What would settle it

An experiment with controlled correlated dephasing noise across shots that finds identical sensitivity scaling for entangled and separable probes would falsify the claimed advantage.

Figures

Figures reproduced from arXiv: 2604.22368 by Anders S{\o}ndberg S{\o}rensen, Anders S. S{\o}rensen, Kasper Hede Nielsen, Noah Kaufmann.

**Figure 1.** Figure 1: (a) Circuit representation of Ramsey spectroscopy using spin-squeezed states. Applying squeezing to the view at source ↗

**Figure 3.** Figure 3: Estimation uncertainty of Ramsey spectroscopy with separable and spin-squeezed input states for different noise view at source ↗

**Figure 4.** Figure 4: The metrological gain r of estimation uncertainties for separable and spin-squeezed protocols for different spatial and temporal noise correlations. The first row and first column of the grid show the considered temporal S(ω) and spatial noise G(k) spectra, respectively, which are combined in the inner plots. From top to bottom and left to right, the spectra are the following: Gaussian, white, linear, and … view at source ↗

**Figure 5.** Figure 5: Dependence of the expectation values most relevant view at source ↗

**Figure 7.** Figure 7: Estimation uncertainty of Ramsey spectroscopy view at source ↗

read the original abstract

Entanglement has been proposed as a means to improve the sensitivity of sensing weak signals. While the degree of this quantum advantage is well understood in noiseless settings, the situation is more complex under realistic conditions, where the system is subject to decoherence. In this case, the enhancement depends on the specific noise characteristics. Previous treatments of colored noise typically assume that the noise is uncorrelated between successive experiments. Here, we consider the scenario in which the noise exhibits correlations across multiple shots. We derive a simple fundamental limit to the sensitivity based on the fact that the sensitivity cannot be better than the signal-to-noise ratio seen by the probe. Focusing on Ramsey spectroscopy with probes affected by pure classical dephasing, we show that, for suitable spatial and temporal noise correlations, entangled probes achieve a better scaling of the sensitivity with the number of probes than separable states. This demonstrates that entanglement can provide a substantial improvement for Ramsey spectroscopy subject to correlated noise.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows entangled states can beat separable scaling in multi-shot Ramsey sensing when dephasing noise correlates across experiments, but the claimed SNR bound needs explicit checking for the entangled case.

read the letter

The key point is that this work drops the usual assumption of uncorrelated shots and finds a regime of spatial and temporal noise correlations where GHZ-like probes give better sensitivity scaling than product states in classical dephasing. The central move is a simple bound: sensitivity cannot exceed the signal-to-noise ratio experienced by the probe itself. They then compare scalings under that bound for different correlation functions and show the advantage appears for suitable choices. That extension to correlated shots is the actual addition over prior colored-noise treatments. The bound itself is clean and the scaling comparison is direct for the cases they pick, which makes the result easy to follow. Credit for focusing on a setting that matches real multi-shot experiments rather than idealized single-shot or uncorrelated noise. The soft spot is the transition of the SNR bound to entangled probes. The derivation likely starts from per-probe or classical averaging arguments, and when noise is shared across the entangled system the joint statistics could change how signal and noise accumulate. The abstract does not flag an explicit verification that the bound survives unchanged, so a referee would want to see the step-by-step application to the entangled density matrix or the accumulated phase distribution. If that step holds without extra approximations, the claim is fine; if it relies on treating the entangled case as a collection of independent probes, the separation of scalings weakens. The paper is aimed at quantum metrology groups that model non-Markovian dephasing in sensors. A reader who already works with Ramsey protocols and wants to know when entanglement survives realistic noise will find the scaling comparison useful and the bound easy to test against their own models. It is solid enough on its own terms to deserve referee time, even if the bound needs tightening. I would send it to peer review and ask the authors to confirm the SNR limit carries over directly to the entangled case under the same correlation functions.

Referee Report

1 major / 1 minor

Summary. The paper claims to derive a simple fundamental limit to the sensitivity of Ramsey spectroscopy based on the signal-to-noise ratio seen by the probe under non-Markovian dephasing with correlations across multiple shots. It shows that for suitable spatial and temporal noise correlations, entangled probes achieve better scaling of sensitivity with the number of probes than separable states, demonstrating a quantum advantage in this correlated noise regime.

Significance. If the result holds, this is significant as it extends the understanding of quantum metrology beyond the usual assumption of uncorrelated noise between experiments. The SNR-based limit provides a clear, simple bound, and the demonstration of improved scaling for entangled states under specific correlations highlights when entanglement can be beneficial despite decoherence. This could have implications for practical quantum sensing applications where noise correlations are present.

major comments (1)

[Derivation of fundamental limit] The bound that 'the sensitivity cannot be better than the signal-to-noise ratio seen by the probe' is central to the claims (see abstract and the section deriving the fundamental limit). However, it is unclear whether this bound, likely derived from per-probe or classical averaging arguments, applies without modification to entangled probes (e.g., GHZ states) when the classical dephasing noise is correlated across both probes and shots. An explicit check or derivation for the entangled case is required to confirm that the scaling advantage is not an artifact of the bound's applicability.

minor comments (1)

[Abstract] The title refers to 'non-Markovian Dephasing' while the abstract specifies 'pure classical dephasing'; clarify if the noise model is strictly classical or includes quantum aspects.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting this important point about the applicability of the fundamental limit. We address the comment in detail below.

read point-by-point responses

Referee: The bound that 'the sensitivity cannot be better than the signal-to-noise ratio seen by the probe' is central to the claims (see abstract and the section deriving the fundamental limit). However, it is unclear whether this bound, likely derived from per-probe or classical averaging arguments, applies without modification to entangled probes (e.g., GHZ states) when the classical dephasing noise is correlated across both probes and shots. An explicit check or derivation for the entangled case is required to confirm that the scaling advantage is not an artifact of the bound's applicability.

Authors: The fundamental limit follows from a general statistical argument: for any probe state (separable or entangled) and any measurement, the variance of an unbiased estimator of the accumulated phase is bounded below by the inverse of the signal-to-noise ratio of the observed outcome distribution. This bound is obtained by applying the Cramér-Rao inequality to the probability distribution of the measurement results under the given noise model; it does not assume independent per-probe averaging or separability. The spatial and temporal correlations enter the calculation of the outcome variance identically for both separable and entangled states, while the signal term (phase sensitivity) scales with the collective operator for GHZ states. We will add an explicit derivation of the bound applied to GHZ states under the correlated dephasing model to the revised manuscript to remove any ambiguity. revision: yes

Circularity Check

0 steps flagged

Fundamental SNR bound independent of entanglement; correlations treated as external conditions

full rationale

The paper states a general limit that sensitivity cannot exceed the probe SNR, presented as a basic fact applying before considering entanglement or specific correlations. The advantage for entangled probes is then shown only for given spatial/temporal correlations (not fitted or derived from the result itself). No self-definitional loops, no parameters fitted then renamed as predictions, and no load-bearing self-citations are evident in the derivation chain. This matches the expected low-circularity case for a paper whose central claim remains independent of its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that sensitivity is bounded by the probe SNR and on the existence of suitable spatial-temporal noise correlations; no free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption The sensitivity cannot be better than the signal-to-noise ratio seen by the probe.
Used to derive the fundamental limit on sensing performance.

pith-pipeline@v0.9.0 · 5483 in / 1236 out tokens · 95887 ms · 2026-05-08T11:57:12.232609+00:00 · methodology

discussion (0)

Reference graph

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[1] [1]

Preparation of a spin-squeezed state; 2.π/2pulse around the collective spinJ y-axis

work page

[2] [2]

Free evolution of the system for a timeτ; 4.π/2pulse around the collective spinJ y-axis

work page

[3] [3]

Measurement of the collective spin componentJz

work page

[4] [4]

This description is in the rotating frame of the field that implements theπ/2Ramsey pulses, which rotates around theJ z-axis with tunable frequencyb p

Repetition of steps 1-5 forL=T /τrepetitions. This description is in the rotating frame of the field that implements theπ/2Ramsey pulses, which rotates around theJ z-axis with tunable frequencyb p. In this frame, the relative phase between the excited and ground states evolves at a frequencybr =b−b p. We assume that the duration of state preparation, meas...

work page

[5] [5]

In this section, we repeat the derivation from Sec

to demonstrate an enhanced uncertainty scaling in the presence of non-Markovian dephasing noise that is uncorrelated between subsequent experiments. In this section, we repeat the derivation from Sec. III using GHZ states as input. For simplicity, we restrict the derivation of the estimation uncertainty and its analysis to spatially uncorrelated noise. Th...

work page

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Preparation of anN-qubit GHZ state|GHZ⟩= 1√ 2 |0⟩⊗N +|1⟩ ⊗N

work page

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Free evolution of the system for a timeτ

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ProjectionmeasurementontotheinitialGHZstate

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Unlike the protocols for separable input states and spin- squeezed input states, this protocol does not involve Ramsey pulses

Repetition of steps 1-3 forL=T /τiterations. Unlike the protocols for separable input states and spin- squeezed input states, this protocol does not involve Ramsey pulses. The parameters of the protocol to op- timize are the operating pointbrτand the interrogation timeτ. Given the combined state of allLexperimental runs andNqubits, we define the measureme...

work page

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K. A. Gilmore, M. Affolter, R. J. Lewis-Swan, D. Barber- ena, E. Jordan, A. M. Rey, and J. J. Bollinger, Quantum- enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals, Science373, 673 (2021)

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