Controlled quantum secure remote sensing

Asad Ali; Mahmood Irtiza Hussain; Muhammad Talha Rahim; Saif Al-Kuwari

REVIEW 4 major objections 4 minor 50 references

Controlled quantum secure remote sensing

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read An N-party GHZ-based remote sensing protocol reaches Heisenberg-limited precision under ideal conditions, and local quantum optimal control restores much of that precision under dephasing and depolarizing noise.

desk verdict The ideal GHZ sensing calculation is standard and sound, but the paper's 'unconditional security' claim depends on a verification step that runs before the parameter is encoded, so the advertised guarantee is not established. read the letter →

arxiv 2504.18102 v2 pith:3BYTL6O2 submitted 2025-04-25 quant-ph

Muhammad Talha Rahim , Saif Al-Kuwari , Mahmood Irtiza Hussain , Asad Ali This is my paper · ORCID

classification quant-ph

keywords securequantumsensingmetrologyGHZstatesHeisenberglimitFisherinformationoptimalcontroldephasingnoisedepolarizing

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes a general N-particle protocol, C-QSRS, in which Alice estimates a single unknown parameter at a remote site by sharing a multiparticle Greenberger-Horne-Zeilinger (GHZ) state with Bob, a semi-trusted sensor who cannot prepare quantum states and is intended to learn nothing about the parameter. In an ideal channel and encoding, the protocol reaches Heisenberg-limited scaling, with the quantum Cramér-Rao bound falling as $1/(p_s N_S^2 t_s^2)$. For non-ideal dynamics, the scheme adds local quantum optimal control (QOC) pulses on Bob's qubits, and a three-qubit numerical analysis shows that the controlled protocol raises both the quantum and classical Fisher information under generalized Pauli dephasing, parallel dephasing, and depolarizing noise. The security mechanism is a pre-encoding verification of the shared GHZ state using $\sigma_x$-parity and $\sigma_z$-equality checks, plus the fact that Bob's reduced state contains no parameter information.

What carries the argument

The load-bearing object is the multiparticle GHZ state $|\Psi_N\rangle = (|0\rangle^{\otimes N}+|1\rangle^{\otimes N})/\sqrt{2}$, split into $N_A$ qubits kept by Alice and $N_S$ qubits sent to Bob, together with the encoding Hamiltonian $H_\omega = (\omega/2)\sum_{j=1}^{N_S}\sigma_z^{(j)}$, which turns the parameter into a relative phase between the two GHZ branches. The security machinery is the two-basis verification: $\sigma_x$ measurements whose outcome product must be $+1$, and $\sigma_z$ measurements whose outcomes must all agree. The noisy-case machinery is the local control Hamiltonian $H_c(t) = \sum_i u_i(t)\sigma_i^{(2)} + \sum_j v_j(t)\sigma_j^{(3)}$ acting only on Bob's qubits, with amplitudes optimized to maximize the quantum or classical Fisher information; tripartite negativity sets the practical evolution time before entanglement is lost.

What would settle it

After the $\sigma_x$-parity and $\sigma_z$-equality checks pass, insert an unknown bias $\beta$ into the Hamiltonian Bob applies; if the checks still pass and Alice's estimate becomes $\omega+\beta$ with unchanged verification statistics, the parameter-integrity claim fails. A numerical version of the same attack in the three-qubit model would settle it without an experiment.

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Extended reading notes

Core claim

The paper's central claim is that entanglement alone can secure remote sensing: an N-qubit GHZ state distributed between Alice and Bob, verified by $\sigma_x$-parity and $\sigma_z$-equality checks, lets Alice estimate a parameter encoded by Bob's evolution under $H_\omega = (\omega/2)\sum_{j=1}^{N_S}\sigma_z^{(j)}$ with Heisenberg-limited precision, while Bob's share never carries the parameter. The noisy extension claims that local time-dependent controls on Bob's qubits, optimized with GRAPE for dephasing and differential evolution for depolarizing noise, increase the achievable quantum and classical Fisher information; in the three-qubit examples the controlled classical Fisher information can even exceed the uncontrolled quantum Fisher information.

Load-bearing premise

The security claim assumes that the pre-encoding GHZ verification checks ($\sigma_x$ parity and $\sigma_z$ equality) catch any tampering with the parameter, including an induced bias that an adversary could insert into Bob's encoding after the checks are done.

Editorial extensions

If this is right

Under ideal conditions the estimation error obeys $(\Delta\tilde{\omega})^2 \approx 1/(p_s N_S^2 t_s^2)$, the Heisenberg limit, so each additional sensing particle improves precision quadratically rather than linearly.
Because tracing out Alice's share leaves Bob with the parameter-independent state $\frac12(|0\rangle\langle0|^{\otimes N_S}+|1\rangle\langle1|^{\otimes N_S})$, Bob cannot learn the parameter from his subsystem alone.
In all considered noise models, including combinations with depolarizing communication noise, the QOC-controlled protocol yields higher quantum and classical Fisher information than the uncontrolled protocol.
The controlled classical Fisher information can surpass the uncontrolled quantum Fisher information, meaning the optimized local measurement extracts more from the noisy state than the best uncontrolled strategy does.
The framework is designed to extend to arbitrary $N$, tunable encoding schemes, and other measurement or LOCC strategies, with the three-qubit cases serving as the numerical demonstration.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Not tested in the paper: since QOC raises Fisher information in generalized Pauli dephasing and depolarizing cases even though tripartite negativity is essentially unchanged, the mechanism is likely protection of specific two-qubit correlations rather than preservation of genuine tripartite entanglement; a bipartite negativity or subsystem QFI diagnostic would test this.
Not tested in the paper: the verification checks occur before encoding, so an adversary who can alter Bob's encoding Hamiltonian after the checks pass could inject an unknown bias into the estimate without tripping the $\sigma_x$-parity or $\sigma_z$-equality tests; a post-encoding check or authenticated encoding Hamiltonian would close that gap.
Not tested in the paper: the ideal Heisenberg scaling is directly testable in current photonic experiments by preparing GHZ states of increasing size and comparing the slope of $\log F_Q$ versus $\log N_S$ with the predicted value of $2$.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The paper does two things: it re-derives the standard Heisenberg-limited sensitivity for an N-party GHZ remote sensing protocol, and it adds local quantum optimal control (QOC) to fight decoherence in a three-qubit example. The first part is textbook; the second is the actual new bit, and it is plausible but not fully supported.

What is good: the ideal-case QFI/CFI calculation is correct. The protocol—Alice distributes a GHZ state, Bob encodes ω via σz on his qubits, Alice measures σx—is clean, and the claim that Bob learns nothing about ω after tracing out Alice's subsystem is right. The noise analysis covers reasonable models (GPD, PPD, depolarizing, with and without a noisy channel), and the plots consistently show QOC improving both QFI and CFI.

The soft spots are real. First, the security argument. The 'parameter integrity' paragraph says an induced bias β is detected by the Pauli-X verification check. But that check is performed on pc copies before the sensing copies run. An adversary who tampers with Bob's Hamiltonian after verification—say, by adding β during the encoding evolution—leaves every verification outcome unchanged and shifts Alice's estimate by β. The paper never addresses this. Even if the bias were injected into the distributed state before verification, a single parity round only detects it with probability (1−cosβ)/2. So the 'unconditional security' claim in the conclusion is not established. The protocol may be secure against some attacks, but the adversary model is unspecified and the proof is missing.

Second, the QOC results are purely numerical: no code, no data, no error bars, and incomplete optimization details (number of GRAPE iterations, DE population, whether curves are best-run or averaged). The noise rates are hand-picked, which is fine, but without reproducibility the central noisy-case claim is hard to verify. This is common in optimal control papers, but it matters because the entire contribution rests on those numbers.

Third, the ideal N-partite protocol overlaps with the authors' own Ref. [14] and earlier GHZ remote sensing work; the novelty is the QOC layer, and that is modest.

Net: the metrology is fine, the QOC idea is reasonable, but the security headline fails as stated. I would not cite this in its current form, but it deserves a serious referee to sort out the adversary model and the numerical reproducibility. Send it to review, expect major revision.

Referee Report

4 major / 4 minor

Summary. The manuscript proposes a controlled quantum secure remote sensing (C-QSRS) protocol. In the ideal setting, Alice (or a trusted external source) distributes an N-partite GHZ state, verifies it with sigma_x parity and sigma_z equality checks, and Bob encodes an unknown parameter omega on his N_S qubits under H_omega = (omega/2) sum_j sigma_z^(j); Alice's final sigma_x measurement yields Heisenberg-limited scaling. For non-ideal dynamics, the paper introduces local quantum optimal control (QOC) pulses on Bob's qubits and reports, for a three-qubit system (N=3, N_A=1, N_S=2), numerical improvements in the quantum and classical Fisher information under generalized Pauli dephasing, parallel dephasing, and depolarizing noise, for both noiseless and noisy communication channels. The paper further claims that the protocol achieves unconditional security, including detection of an adversary-induced parameter bias beta.

Significance. The ideal-case protocol is a straightforward GHZ-based remote sensing scheme, and the reported Heisenberg-limited variance scaling of Eq. (16) appears correct. The more novel contribution is the numerical study of local QOC as a noise-mitigation tool for secure remote sensing; if the reported gains are reproducible, the idea is of interest to the quantum sensing and quantum communication communities. I also note that the metric comparison is not circular: the uncontrolled baseline is computed independently of the QOC optimization, and the noise rates are fixed model parameters rather than fitted to the target results. However, the security claim is not established by the presented verification argument, and the numerical results are not reproducible from the manuscript as written, so the advertised conclusions currently outrun the evidence.

major comments (4)

[Sec. III, 'Parameter integrity'] The claim that an induced bias beta is detected by the sigma_x parity verification is not supported. The parity and equality checks are performed on the distributed GHZ states before the encoding step, as stated in Sec. III ('Controlled security check'). An adversary who replaces H_omega in Eq. (13) by H_{omega+beta} during Bob's evolution leaves every pre-encoding verification outcome unchanged while shifting the phase in Eq. (14) to N_S(omega+beta)t_s/2; Alice then silently estimates omega+beta with no detection event. Even under the more favorable interpretation that the bias is inserted into the distributed state before verification, a single sigma_x parity round rejects only with probability (1-cos(beta))/2, so detection is probabilistic rather than guaranteed. The Conclusion's 'unconditional security' therefore requires either a formal attack model that includes post-verification parameter tampering, or a substantially weakened security claim.
[Sec. IV, Figs. 4-5] The central quantitative claim that local QOC improves the QFI and CFI rests entirely on numerical simulations whose details are not reported. The paper specifies the control Hamiltonian in Eq. (19) and names GRAPE and differential evolution as optimizers, but it does not give the time discretization, number of control intervals, amplitude bounds, convergence tolerances, number of independent optimization runs, or the resulting optimal control pulses. Figures 4 and 5 contain no error bars or convergence data, and the data availability statement only offers code 'upon reasonable request.' Under standard reproducibility expectations, the reported C-QFI and C-CFI values cannot be verified from the manuscript; the authors should provide code and data, or at minimum a detailed optimization appendix with all hyperparameters.
[Sec. IV, QFI computation] For the noisy mixed states, the paper never states how the QFI is computed numerically. Equation (5) gives the SLD expression in the eigenbasis of rho, but the manuscript does not specify how F_Q(rho_omega) is evaluated for the Lindblad-evolved density matrices used in Secs. IV.C.1-IV.C.3, nor how the derivative partial_omega rho is obtained. Since the QFI is the primary metric in Figures 4 and 5, the numerical method (e.g., spectral decomposition with finite-difference derivatives, or an exact SLD formula) must be described to make the results checkable.
[Sec. III, 'Controlled security check' and Conclusion] The protocol does not quantify the number of verification rounds p_c needed for any claimed security level. The text states that p_c states are randomly chosen for sigma_x and sigma_z tests, but no relation is derived among p_c, the detection probability for a malicious modification, and an adversary's success probability. With finite p_c the guarantee is statistical, not 'unconditional,' and the Conclusion's use of 'unconditional security' is therefore too strong. A finite-resource security statement, or a clearly delimited asymptotic claim, is needed.

minor comments (4)

[Eq. (16)] The notation in Eq. (16) is inconsistent: the first expression uses sin^2(N_S omega t_s), while the denominator uses sin(N_S omega t), and the final identity should read 1/(p_s N_S^2 t_s^2). The variable t_s should be used consistently throughout the equation.
[Sec. III, 'Secure parameter teleportation'] The statement that the scheme achieves Heisenberg-limited scaling should be qualified: the variance in Eq. (16) scales as (N_S t_s)^-2, not (N t_s)^-2, because the N_A ancilla qubits held by Alice do not enter the encoded phase. This is asymptotically equivalent to HL when N_S is proportional to N, but for finite N the precise statement differs from 'N-particle HL scaling.'
[Sec. IV.C, tripartite negativity] The paper reports in Sec. IV.C.1 and IV.C.3 that QOC does not improve tripartite negativity, while Figures 4 and 5 show substantial QOC gains in Fisher information. This apparent tension is never addressed; a brief explanation (e.g., that local controls can protect parameter-sensitive coherences without increasing genuine tripartite entanglement) would improve the reader's understanding.
[Sec. IV.B.2.b, Eq. (21)] The density-matrix elements in Eq. (21) contain absolute values such as |(4-3Gamma)Gamma|, which is unusual for a valid physical state. Clarify whether these expressions assume Gamma in a particular range or whether the absolute values are part of the state definition; as written, the positivity and smoothness of the state as a function of Gamma are unclear.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the ideal-protocol Heisenberg scaling is derived directly from the stated GHZ state and Hamiltonian, and the QOC improvements are an optimization benchmark rather than a fitted prediction. The only minor self-citation is non-load-bearing, and the security caveat is a correctness concern, not circularity.

full rationale

The paper's ideal-protocol derivation is self-contained: starting from the GHZ state in Eq. (11) and the encoding Hamiltonian Hω in Eq. (13), the evolved state in Eq. (14) and the σx measurement statistics lead directly to the quantum Cramer-Rao bound expression in Eq. (16). No parameter is fitted to the target result, and the Heisenberg-limited scaling 1/(ps NS^2 ts^2) follows by direct calculus from the stated state, so this step is not circular. The noisy-protocol section optimizes the time-dependent control amplitudes in Hc(t) (Eq. 19) with the QFI and CFI as objective functions and then reports these same QFI and CFI values. This is a numerical optimization benchmark, not a prediction derived from a fitted model; the uncontrolled case is the zero-control point, so the controlled-versus-uncontrolled comparison is a legitimate baseline. The noise rates (γgp, γz, γd, Γ) are explicitly chosen model parameters, not fitted to the reported QFI or CFI values. The only self-citation, Ref. [14] by the first author, appears in the introductory background on existing SQS protocols and is not load-bearing for the new derivation or for the noise analysis. One passage in Sec. III ('Parameter integrity') asserts that an induced bias β can be detected by the Pauli-X verification step, but the verification is performed before the encoding evolution, so an attack mounted after verification would not be detected; this is a security-support gap, not a circular derivation step, and it does not raise the circularity score. Overall, no derivation step reduces by construction to its own input, and the central sensing result is independently derived from the stated quantum state and measurement setup.

Assumptions & free parameters 8 free parameters · 7 assumptions · 0 invented entities

The analysis assumes standard quantum estimation theory (QFI/SLD, Cramér-Rao bounds), a Markovian Lindblad master equation, specific noise models (GPD, PPD, DP, asymmetric depolarization), and a security model in which a semi-trusted Bob is verified by GHZ parity checks. The noise rates and the NA=1, NS=2 split are hand-chosen; no new entities are introduced. The weakest load-bearing assumption is that the verification measurements also certify parameter integrity against bias attacks.

free parameters (8)

γ_gp = 0.05
GPD dephasing rate in Sec. IV.C.1, chosen by hand.
γ_z = 0.025
PPD dephasing rate in Eq. (22), chosen by hand.
γ_d = 0.02
Depolarizing rate in Eq. (23), chosen by hand.
Γ = 0.06
Asymmetric depolarization strength for Alice-as-source channel (Eq. 21), chosen by hand.
λ = not reported
Depolarizing noise strength for the external-source channel; referenced in Sec. IV.B but no numeric value is given for simulations.
T_f = 8.0
Maximum evolution time for depolarizing scenarios, set when tripartite negativity reaches zero (Sec. IV.C.3).
θ, φ = θ=π/4, φ=0
Direction of the GPD Lindblad operator (Sec. IV.C.1), chosen by hand.
NA, NS = NA=1, NS=2
Number of ancilla and sensing qubits in the noisy scenario, chosen for computational tractability (Sec. IV).

assumptions (7)

domain assumption The sensing dynamics is Markovian and described by a Lindblad master equation with time-dependent controls (Eq. 9).
Sec. II.B. Memoryless approximation is valid only if environmental correlation times are short; non-Markovian effects are deferred.
domain assumption The unknown parameter acts via Hω = (ω/2) Σ_{j=1}^{NS} σ_z^(j) on Bob's sensing qubits only (Eq. 13).
Sec. III. This encoding choice yields the ideal Heisenberg scaling; other encodings would give different results.
domain assumption The communication link is a depolarizing channel, either uniform (external source) or asymmetric (Alice as source), as in Sec. IV.B.
Standard model, but the noise strength values (Γ, λ) are chosen by hand; no physical justification is given.
ad hoc to paper The GHZ verification step (σx parity and σz equality checks) certifies both channel security and parameter integrity, including detection of an induced bias β.
Sec. III, Parameter integrity. The statement is asserted, not proven; tampering after verification would escape detection.
ad hoc to paper Local controls Hc(t)=Σ_i u_i(t) σ_i^(2) + Σ_j v_j(t) σ_j^(3) on Bob's two qubits are sufficient to reach the reported optima.
Sec. IV.A.1. No reachability or optimality proof; the control axes are chosen without justification.
standard math The SLD QFI formula (Eq. 5) and the quantum and classical Cramér-Rao bounds (Eqs. 2-3) are valid for the mixed states involved.
Sec. II.A. Standard quantum estimation theory.
domain assumption Alice and Bob have perfect quantum memories.
Sec. IV, opening paragraph. This avoids memory decoherence and is an idealization.

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Pith. "Pith review of Controlled quantum secure remote sensing." pith.science (2026). https://pith.science/paper/3BYTL6O2

@misc{pith2026250418102,
  author       = {Pith},
  title        = {Pith review of: Controlled quantum secure remote sensing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3BYTL6O2}},
  note         = {Machine review of arXiv:2504.18102}
}

abstract

Quantum resources enable secure quantum sensing (SQS) of remote systems, offering significant advantages in precision and security. However, decoherence in the quantum communication channel and during the evolution of quantum states can erode these advantages. In this work, we first propose a general $N-$particle scheme that achieves Heisenberg-limited (HL) scaling for single-parameter estimation in the presence of an ideal quantum communication channel and encoding scenario. For non-ideal dynamics, we introduce a modified protocol incorporating local quantum optimal control (QOC) operations to address noise in SQS under generalized Pauli dephasing and parallel dephasing noise. We analyze two distinct scenarios: a noiseless communication channel with noisy evolution, and a noisy communication channel with noisy evolution. For the noisy channel, we model the link between the communicating parties as a depolarizing channel. The protocol leverages QOC operations to actively mitigate noise, enhancing the achievable quantum Fisher information (QFI) and the classical Fisher information (CFI) based on the chosen measurement strategy.

Figures

Figures reproduced from arXiv: 2504.18102 by the authors.

**Figure 2.** FIG. 2. The QOC process applied locally by Bob, who possesses the noisy channel to be probed. After the evolution, Alice [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3. Comparison of the tripartite negativity ( [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. Comparison of QFI and CFI for the cases of (i) noiseless communication and noisy evolution, (ii) noisy communication [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. The performance of QFI and CFI under depolarizing noise represented by the Fisher information (FI) versus total [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

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R. Demkowicz-Dobrzański and L. Maccone, Phys. Rev. Lett. 113, 250801 (2014)

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[2] [1]

A trusted exter- nal source generates and distributes entanglement between Alice and Bob

External Source Distribution. A trusted exter- nal source generates and distributes entanglement between Alice and Bob

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[3] [2]

Alice locally prepares the entangled state and distributes the required qubits to Bob

Alice as the Source . Alice locally prepares the entangled state and distributes the required qubits to Bob. While both cases lead to identical quantum sensing steps under ideal conditions, their distinctions become relevant when we consider noisy quantum channels. The general structure of the proposed protocol is summarized in Fig. 1. The protocol consis...

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[4] [3]

Control Hamiltonian To counteract the detrimental effects of noise, we em- ploy a time-dependent local quantum optimal control Hamiltonian of the form Hc(t) = 3∑ i=1 ui(t)σ(2) i + 3∑ j=1 vj(t)σ(3) j , (19) where{σ0,σ 1,σ 2,σ 3} ={I,σx,σy,σz} and σ(n) i denotes the i-th Pauli operator acting on then-th qubit. Here, the control acts locally on Bob’s two qub...

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[5] [4]

For a system of three qubitsA, B1, andB2, we compute negativities for the bipartitions A|B1B2, AB 1|B2, AB 2|B1

Tripartite Negativity In our analysis, we benchmark the optimal evolution time by quantifying genuine tripartite entanglement us- ing tripartite negativity. For a system of three qubitsA, B1, andB2, we compute negativities for the bipartitions A|B1B2, AB 1|B2, AB 2|B1. For any bipartition X | Y, the bipartite negativity is defined as [30] NX|Y = ‖‖ρTX XY ...

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[6] [5]

This situation is plau- sible when Alice and Bob implement effective entangle- ment purification steps [32, 33] prior to the noisy evolu- tion stage

Noiseless Communication and Noisy Encoding In this scenario, we assume that the communication channels exhibit little to no noise. This situation is plau- sible when Alice and Bob implement effective entangle- ment purification steps [32, 33] prior to the noisy evolu- tion stage. Specifically, the initial state is prepared as a 7 tripartite GHZ state as i...

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[7] [6]

Noisy Communication and Noisy Evolution In this scenario, we have two cases based on whether Alice is the source or the source is external. a. External Source. In this scenario, the communi- cation channel introduces uniform noise to each qubit via a depolarizing channel. The channel is characterized by the map E(ρ) = (1−λ)ρ +λI d, where ρ =|Ψ⟩⟨ Ψ|, with|...

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[8] [7]

In this model, dephasing is not restricted to a single direction but is represented by a combination of the Pauli matricesσx, σy, andσz

Generalized Pauli Dephasing Noise Generalized Pauli dephasing (GPD) noise in quantum metrology involves phase fluctuations affecting the quan- tum state along multiple axes. In this model, dephasing is not restricted to a single direction but is represented by a combination of the Pauli matricesσx, σy, andσz. The dynamics of a system subject to GPD noise ...

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