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arxiv: 2605.22917 · v1 · pith:HNSEBQFMnew · submitted 2026-05-21 · 🪐 quant-ph · cond-mat.stat-mech

Quantum Fisher Information under decoherence with explicit wavefunctions

Francesco Musso , Vittorio Vitale , Sara Murciano This is my paper

Pith reviewed 2026-05-25 05:49 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords quantum fisher informationdecoherencemany-body wave functionsmarkov chain monte carlojastrow-gutzwillerquantum metrologynoise channels
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The pith

For analytically known many-body wave functions, lower bounds on the quantum Fisher information in the presence of decoherence map directly onto classical expectation values.

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

The paper develops a method to estimate lower bounds on the quantum Fisher information for many-body states subject to decoherence. When the wave function is known analytically in the occupation-number basis, these bounds convert into averages over a classical probability distribution built from the amplitudes. Markov-chain Monte Carlo sampling then evaluates the bounds at a cost that grows only as a slow exponential in system size. The approach is worked out in detail for Jastrow-Gutzwiller states under local dephasing, local amplitude damping, and global depolarizing noise, and polynomial versus Krylov lower bounds are compared for each channel.

Core claim

Systematic lower bounds to the QFI can be mapped onto expectation values over a classical probability distribution defined by the wave function amplitudes. This mapping enables efficient estimation via Markov-chain Monte Carlo sampling, with a computational cost that scales as a slow exponential (e^{b L} with b ≲ 0.6) and remains manageable for system sizes well beyond exact diagonalization. The framework is specified to Jastrow-Gutzwiller wave functions and applied to three noise channels.

What carries the argument

The mapping of QFI lower bounds to classical expectation values over the probability distribution of wave-function amplitudes.

If this is right

  • The sampling cost remains manageable up to system sizes where exact diagonalization fails.
  • Polynomial and Krylov-based lower bounds can be compared by relating their performance to the effective rank of the noisy density matrix.
  • The metrological content of Jastrow-Gutzwiller states is characterized through the observables that maximize the QFI and the scaling of that maximum with system size L.
  • The same reduction applies to other analytically known wave functions and to information-theoretic quantities beyond the QFI.

Where Pith is reading between the lines

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

  • The classical mapping may extend to other measures of quantum information whenever the wave function supplies an explicit amplitude distribution.
  • Large-system simulations made possible by this method could identify which noise channels most strongly limit metrological utility in practice.
  • The framework invites direct numerical checks on additional families of analytic wave functions to test how general the slow-exponential scaling remains.

Load-bearing premise

The wave functions must be known analytically in the occupation-number basis so that the probability distribution of amplitudes is directly accessible.

What would settle it

For any small system where both the direct QFI lower bound and the mapped classical expectation can be computed exactly, the two quantities must agree within Monte Carlo error; systematic mismatch falsifies the reduction.

Figures

Figures reproduced from arXiv: 2605.22917 by Francesco Musso, Sara Murciano, Vittorio Vitale.

Figure 1
Figure 1. Figure 1: FIG. 1. Numerical results on the bounds to the QFI for the dephased JG wave function for different values of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Numerical results on the bounds to the QFI for the damped JG wave function for different values of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Numerical results for the bounds on the QFI of the depolarized JG wave function for [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Correlation function of the JG wave functions in the critical regime. For [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Number of the Markov chain samples of the JG distribution, for different values of [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
read the original abstract

We present a method to estimate the quantum Fisher information (QFI) of many-body quantum states in the presence of decoherence, where its direct evaluation requires the full spectral resolution of the density matrix. We show that, for many-body wave functions known analytically in the occupation-number basis, systematic lower bounds to the QFI can be mapped onto expectation values over a classical probability distribution defined by the wave function amplitudes. This mapping enables efficient estimation via Markov-chain Monte Carlo sampling, with a computational cost that scales as a `slow' exponential ($e^{b L}$ with $b \lesssim 0.6$) and remains manageable for system sizes well beyond exact diagonalization. We specify this framework to Jastrow-Gutzwiller wave functions. We characterize their metrological content by identifying the observables that maximize the QFI and the corresponding scaling with $L$. Then, we analyze the QFI under three physically motivated noise channels: local dephasing, local amplitude damping, and global depolarizing. We compare polynomial and Krylov-based lower bounds across these channels, relating their behavior to the effective rank of the noisy density matrix and to the structure of the operator generating the parameter encoding. The framework extends naturally to other analytically known wave functions and to a broader class of information-theoretic quantities beyond the QFI.

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.

Referee Report

0 major / 2 minor

Summary. The manuscript introduces a method to estimate lower bounds on the quantum Fisher information (QFI) for many-body states under decoherence when the pure-state wave function is known analytically in the occupation-number basis. Systematic lower bounds are mapped to expectation values over the classical probability distribution |c_n|^2, enabling Markov-chain Monte Carlo estimation whose cost scales as e^{b L} with b ≲ 0.6. The framework is specialized to Jastrow-Gutzwiller wave functions; optimal observables and their L-scaling are identified, after which the QFI is analyzed under local dephasing, local amplitude damping, and global depolarizing channels. Polynomial and Krylov-based lower bounds are compared and related to the effective rank of the noisy density matrix and the structure of the generator.

Significance. If the mapping and its extension to the three noise channels are correct, the work supplies a concrete computational route to metrological bounds on analytically tractable many-body states at sizes inaccessible to exact diagonalization. The explicit restriction to occupation-basis analytic wave functions, the concrete application to Jastrow-Gutzwiller states, and the comparison of bound constructions tied to effective rank constitute useful contributions. The claimed slow-exponential scaling, once validated numerically in the text, would be a practical strength for the field.

minor comments (2)
  1. The abstract states the scaling b ≲ 0.6; the main text (likely §4 or the numerical-results section) should report the fitted exponents obtained for the Jastrow-Gutzwiller states under each channel so that readers can assess how robustly the bound holds.
  2. Notation for the classical probability distribution and the precise form of the lower-bound mapping should be introduced with an equation number in the methods section to facilitate direct comparison with the subsequent noise-channel calculations.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. The referee's summary accurately captures the core contribution: a Monte Carlo mapping of QFI lower bounds to classical expectations for analytically known occupation-basis wave functions, with explicit application to Jastrow-Gutzwiller states and analysis under three decoherence channels. No specific major comments were provided in the report, so we address the overall evaluation below and note that we will incorporate minor clarifications as needed in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper derives a mapping from QFI lower bounds to classical expectation values over the probability distribution of wavefunction amplitudes |c_n|^2 for states known analytically in the occupation-number basis. This enables MCMC estimation with claimed scaling. The construction is presented as a direct computational reduction from the given analytic wavefunctions (Jastrow-Gutzwiller) under specified noise channels, without any equations reducing the claimed bounds to fitted parameters by construction, self-citations that are load-bearing for the central result, or ansatzes smuggled via prior work. The weakest assumption (analytic knowledge of the wavefunction) is stated explicitly and does not create a self-definitional loop. The result is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that wavefunctions are analytically known in the occupation-number basis and that QFI lower bounds admit an exact rewriting as classical expectation values; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Wave functions are known analytically in the occupation-number basis
    Required for the probability distribution of amplitudes to be directly usable in the mapping.
  • domain assumption Systematic lower bounds to the QFI admit an exact mapping to classical expectation values
    Core premise that converts the quantum problem into a classical sampling problem.

pith-pipeline@v0.9.0 · 5764 in / 1444 out tokens · 26649 ms · 2026-05-25T05:49:05.625239+00:00 · methodology

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    QFI of the GHZ and Dicke states Let us consider the GHZ state |GHZ⟩= 1√ 2 (|ψeven⟩+|ψ odd⟩),(C15) where|ψ even⟩=|0101. . .01⟩and|ψ odd⟩=|1010. . .10⟩. The corresponding density matrix, written in the occupation number basis as in Eq. C2, is just a 2 by 2 matrix with all elements equal to1/2. Using the results of Eq. 16, we know that applying the local dep...

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    PY a=1 c2 na # X qa:q a⊆na |qa|=k

    Monte Carlo estimator of the density matrix moments Oncemore, inthecomputationoftheQFIbounds, weareinterestedincalculating, throughMonteCarlointegration, the momentsTr(ρrOρsO). Similarly to the calculations for the dephased state, we setP=r+sand we have Tr ρr pOρs pO = X q1,...,qp " PY a=1 p|qa|(1−p) N−|q a| # Tr | ˜ψq1 ⟩⟨ ˜ψq1 | · · · |˜ψqr ⟩⟨ ˜ψqr |O| ˜...

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  67. [67]

    |GHZ⟩= 1√ 2 (|ψeven⟩+|ψ odd⟩),(D18) where|ψ even⟩=|0101

    Analytical result for the QFI of the GHZ state Let us consider a system ofLqubits prepared in the GHZ state. |GHZ⟩= 1√ 2 (|ψeven⟩+|ψ odd⟩),(D18) where|ψ even⟩=|0101. . .01⟩and|ψ odd⟩=|1010. . .10⟩. For each branch|ψ σ⟩(withσ∈ {even,odd}), we define the following sets: •n σ: the set of occupied sites without noise (|nσ|=L/2), •q σ: the set of particles los...

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  68. [68]

    Considering the QFI in Eq. 1 with the staggered magnetization operator OZ = 1 2 PL j=1(−1)jZj, we note that sinceOis diagonal in the computational basis, all pairs of diagonal eigenstates |mσ⟩give⟨m σ|O|m′ σ′⟩= 0form σ ̸=m ′ σ′. The only non-vanishing contribution comes from the|GHZ⟩state. We obtain FQ[ρ′, O] = (1−p) L/2 FQ[ρ, O],(D22) whereF Q[ρ, O] =L 2...

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