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arxiv: 2604.06303 · v2 · submitted 2026-04-07 · 🪐 quant-ph · gr-qc· hep-th

Optimization of entanglement harvesting with arbitrary temporal profiles: the limit of second order perturbation theory

Marcos Morote-Balboa , T. Rick Perche This is my paper

Pith reviewed 2026-05-10 18:35 UTC · model grok-4.3

classification 🪐 quant-ph gr-qchep-th
keywords entanglement harvestingscalar quantum fieldtemporal profilesHermite expansionnegativityperturbation theoryoptimizationsignaling conditions
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The pith

Optimizing arbitrary temporal profiles via Hermite expansion increases entanglement harvesting by orders of magnitude.

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

The paper examines how two local probes harvest entanglement from the vacuum of a real scalar quantum field when their couplings have arbitrary time dependence. The authors use a Hermite expansion of those profiles to compute the smeared field propagators in closed form and recast the negativity between the probes as a matrix product that can be optimized numerically. They carry out this optimization under different constraints on whether the probes can signal to each other and obtain entanglement enhancements of several orders of magnitude. A sympathetic reader would care because the result suggests that current experimental proposals for vacuum entanglement could be made far more effective, even though the stronger couplings needed would leave the usual weak-coupling regime.

Core claim

We study the protocol of entanglement harvesting when two local probes couple to the vacuum of a real scalar quantum field with arbitrary temporal profiles. We use a Hermite expansion to efficiently compute smeared field propagators in closed-form, recasting the negativity between the probes as a matrix product. We then optimize the protocol under different signalling conditions, enhancing entanglement harvesting by several orders of magnitude. This optimization would take current experimental proposals beyond the regime of second order perturbation theory.

What carries the argument

Hermite expansion of the temporal profiles that yields closed-form expressions for the smeared field propagators, allowing the negativity to be written as a matrix product whose eigenvalues can be maximized under signaling constraints.

Load-bearing premise

The Hermite expansion accurately captures the relevant physics for the chosen profiles and higher-order perturbative corrections remain negligible even after optimization increases the coupling strength or interaction time.

What would settle it

A direct calculation or experiment in an optimized setup showing that the harvested negativity fails to increase by the predicted orders of magnitude or that higher-order terms become large enough to suppress the entanglement.

Figures

Figures reproduced from arXiv: 2604.06303 by Marcos Morote-Balboa, T. Rick Perche.

Figure 1
Figure 1. Figure 1: Negativity and signalling contribution for two iden [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Maximum negativity for detectors separated by a [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Maximum negativity Ne + for detectors separated by a distance of L = 5T0 on the subspace spanned by {hn,N }N as a function of N. as N + ∼ λ 2√ Nosc, with Nosc being the number of oscil￾lations of the function. Given that our basis expansion spans all compactly supported switching functions in the limit N → ∞, we can conclude that [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: Plot of the maximizing functions of Ne within the subspace spanned by {hn,N }N for detectors separated by a distance of L = 5T0. In [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Maximum eigenvalue of ∆ within the subspace spanned by {hn,N }N for detectors separated by a distance of L = 5T0 as a function of N for different values of Ω. In [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Negativity plot for the optimal approximately dis [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Spacetime depiction of the optimal switching func [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Negativity and signalling contribution for the [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
read the original abstract

We study the protocol of entanglement harvesting when two local probes couple to the vacuum of a real scalar quantum field with arbitrary temporal profiles. We use a Hermite expansion to efficiently compute smeared field propagators in closed-form, recasting the negativity between the probes as a matrix product. We then optimize the protocol under different signalling conditions, enhancing entanglement harvesting by several orders of magnitude. This optimization would take current experimental proposals beyond the regime of second order perturbation theory.

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

1 major / 2 minor

Summary. The manuscript studies entanglement harvesting from a real scalar quantum field using two local probes with arbitrary temporal profiles. It introduces a Hermite expansion of the smearing functions to obtain closed-form expressions for the smeared propagators, recasts the harvested negativity as a matrix product, and optimizes the profiles under different signalling conditions. The central claim is that this optimization enhances the harvested negativity by several orders of magnitude and pushes the relevant parameters outside the validity regime of second-order perturbation theory.

Significance. If the optimization results and the claimed enhancement hold under a properly validated perturbative regime, the work would provide a concrete, computationally efficient route to substantially stronger entanglement harvesting protocols. The technical device of Hermite expansions yielding closed-form propagators and a matrix-product expression for negativity is a clear methodological advance that could be reused in related relativistic quantum information calculations.

major comments (1)
  1. [Abstract and optimization results] Abstract and the optimization section: the claim that the optimized protocols lie outside the regime of validity of second-order perturbation theory is not supported by any explicit comparison of the perturbative parameter (coupling strength times interaction duration) before versus after optimization, nor by an estimate of the size of fourth-order Dyson terms relative to the retained second-order contribution for the new profiles. Because the entire optimization is performed inside the second-order expressions, this omission directly undermines the central assertion that the results exit the perturbative regime.
minor comments (2)
  1. [Methods] The manuscript would benefit from an explicit statement of the range of Hermite truncation orders used and a brief convergence check against the exact propagator for at least one representative profile.
  2. [Results] Notation for the negativity matrix elements and the signalling conditions could be clarified with a short table summarizing the different cases considered.

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 perturbative regime. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract and optimization results] Abstract and the optimization section: the claim that the optimized protocols lie outside the regime of validity of second-order perturbation theory is not supported by any explicit comparison of the perturbative parameter (coupling strength times interaction duration) before versus after optimization, nor by an estimate of the size of fourth-order Dyson terms relative to the retained second-order contribution for the new profiles. Because the entire optimization is performed inside the second-order expressions, this omission directly undermines the central assertion that the results exit the perturbative regime.

    Authors: We agree that an explicit comparison is needed to substantiate the claim. In the revised manuscript we will add, in the optimization section, a direct comparison of the perturbative parameter (coupling strength times interaction duration) evaluated on the unoptimized versus optimized profiles. We will also include a qualitative estimate of the relative magnitude of fourth-order contributions based on the scaling of the Dyson series and the structure of the two-point functions, while noting that a complete fourth-order calculation for arbitrary profiles remains beyond the scope of the present work. These additions will either support or appropriately qualify the statement in the abstract. revision: yes

Circularity Check

0 steps flagged

No circularity: optimization is a direct numerical procedure on explicitly derived second-order expressions

full rationale

The paper derives closed-form smeared propagators via Hermite expansion of the temporal profiles, recasts the negativity matrix elements as a matrix product, and performs numerical optimization over the expansion coefficients under fixed signalling conditions. All steps are forward computations from the standard second-order perturbative formulas for the negativity; no fitted parameter is relabeled as a prediction, no self-citation supplies a load-bearing uniqueness theorem, and the final claim that the optimized protocols lie outside the perturbative regime is an external validity statement rather than a definitional reduction. The derivation chain is therefore self-contained and does not collapse to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate free parameters, axioms, or invented entities; standard QFT vacuum assumptions are implicit but not specified.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Bipartite entanglement harvesting with multiple detectors

    quant-ph 2026-04 unverdicted novelty 5.0

    Multiple Unruh-DeWitt detectors harvest more vacuum entanglement when arranged in specific configurations, with harvested negativity scaling linearly in linear chains.

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    erfi |L| −t 0 −i(Ω 1T 2 1 −Ω 2T 2 2 )√ 2 p T 2 1 +T 2 2 +σ 2 1 +σ 2 2 ! + e − (t0+|L|+i(Ω1 T2 1 −Ω2 T2 2 ))2 2(T2 1 +T2 2 +σ2 1+σ2

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  78. [78]

    e− (L+vT 2)2 4T2 erfi L+vT 2 2T + e− (L−vT 2)2 4T2 erfi L−vT 2 2T # = Te −Ω2T 2 4L√π e 1 4 T 2u2 e−iΩT 2u

    erfi |L|+t 0 + i(Ω1T 2 1 −Ω 2T 2 2 )√ 2 p T 2 1 +T 2 2 +σ 2 1 +σ 2 2 !# , (A4) ∆(f1, f2) =− T1T2ei(Ω1t1+Ω2t2)e− Ω2 2 T2 2 2 − Ω2 1 T2 1 2 2 √ 2π|L| p T 2 1 +T 2 2 + 2σ2 " e − (t0 −|L|+i(Ω1 T2 1 −Ω2 T2 2 ))2 2(T2 1 +T2 2 +2σ2) erf |L|(T 2 1 +T 2 2 )+2σ2(t0+i(Ω1T 2 1 −Ω2T 2 2 )) 2σ √ T 2 1 +T 2 2 √ T 2 1 +T 2 2 +2σ2 + e − (t0+|L|+i(Ω1 T2 1 −Ω2 T2 2 ))2 2(T2...

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