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REVIEW 2 major objections 4 minor 80 references

The effect of curvature on local observables in quantum field theory

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Pith's one-line read The smeared variance of a massless scalar field picks up a universal curvature term built from $R$ and $R_{00}$ plus a state constant, and the correction flows into gapless particle-detector response.

desk verdict The paper has a sign error that flips the headline curvature coefficient; the idea is sound but the main formula needs a re-derivation. read the letter →

arxiv 2412.12294 v3 pith:I4DZ2W6A submitted 2024-12-16 quant-ph gr-qchep-th

Ahmed Shalabi , Matheus H. Zambianco , T. Rick Perche This is my paper · ORCID
classification quant-phgr-qchep-th MSC 81T2083C47 PACS 04.62.+v03.70.+k
keywords quantumfieldtheoryincurvedspacetimeHadamardstatesRiemannnormalcoordinatessmearedobservablesUnruh-DeWittdetectorsvacuumfluctuationsmasslessscalargapless
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

This paper derives the leading-order imprint of spacetime curvature on the most basic nontrivial measurement one can make with a quantum field: the variance of the field amplitude in a small spacetime region. Working with a massless real scalar field in a quasifree Hadamard state, the authors show that a Gaussian probe of size $\ell$ yields an expectation value that splits into the flat-space value $1/(16\pi^2\ell^2)$, a purely geometric curvature correction combining the Ricci scalar $R$, its time-time component $R_{00}$, and a numerical constant, plus a state-dependent constant. The geometric part is universal across Hadamard states at this order, while the quantum state enters only through the constant. Because a gapless Unruh-DeWitt detector's final state is determined entirely by this variance, the same correction appears directly in the detector's statistics. This is an explicit closed-form bridge from the well-studied Hadamard short-distance structure of two-point functions to physically measurable local observables.

What carries the argument

Three pieces carry the argument. The first is Riemann normal coordinates centered at the probe's center event $z$: they let the authors import the same Gaussian smearing function used in Minkowski space, and they give the short-distance expansion of Synge's world function, $\sigma(x,x') \approx \frac12\eta_{ab}(x-x')^a(x-x')^b + \frac16 R_{acbd}(z)x^a x^b x'^c x'^d$, whose derivative terms feed every curvature correction. The second is the Hadamard parametrix $W(x,x') = \Delta^{1/2}/(8\pi^2\sigma) + v\ln(\sigma/\ell_0^2) + w$, with the Van Vleck determinant $\Delta$, the geometric coefficient $v_0 = R/12$, and the state-dependent coefficient $w_0$; this is what converts the Hadamard short-distance structure into explicit curvature corrections to the two-point function. The third is the Gaussian spacetime smearing $\Lambda(x)$ with $T = \sigma = \ell$, which makes every integral in the expansion explicitly computable and reduces the Riemann and Ricci tensor corrections to $-(5R+3R_{00})/(576\pi^2)$. The bridge to measurement is the gapless Unruh-DeWitt detector, whose interaction Hamiltonian density satisfies $[[\hat h_I(x),\hat h_I(x')],\hat h_I(x'')]=0$, so the Magnus expansion terminates and the final state is exactly a function of $\xi = \lambda^2\langle\hat\phi(\Lambda)^2\rangle_\omega$ — which is why the curvature correction to field variance immediately becomes a curvature correction to detector statistics.

What would settle it

Take a spacetime with an exactly known Hadamard state, for instance de Sitter space in the Bunch-Davies vacuum, and compute the smeared expectation value $\langle\hat\phi(\Lambda)^2\rangle_\omega$ for the Gaussian probe of width $\ell$ directly from the exact Wightman function. Subtract the flat-space value $1/(16\pi^2\ell^2)$ and compare the residual with $-(5R+3R_{00})/(576\pi^2) + (R/12)P_{\ln} + \omega_\Lambda$ as $\ell$ ranges over values small compared with the curvature radius: the formula predicts an $\ell$-independent match with deviations scaling as $\ell^2\ln\ell$. A residual that depends on the hard cutoff of the Gaussian tails, or that does not converge to the predicted constant as $\ell\to 0$, would falsify the central claim.

Watch

Extended reading notes

Core claim

The central result is Eq. (38): for a massless real scalar field and a Gaussian spacetime smearing with equal temporal and spatial width $\ell$, centered at an event $z$ in Riemann normal coordinates, the smeared squared-field expectation value in a quasifree Hadamard state $\omega$ is $$\langle \hat\$\varphi$(\Lambda)^2\rangle_\omega = \frac{1}{16\$pi^{2}$\$ell^{2}$} - \frac{5R + 3R_{00}}{576\$pi^{2}$} + \frac{1}{12}R\,P_{\ln} + \omega_\Lambda + O(\$ell^{2}$\ln\ell)$$ where $R$ is the Ricci scalar and $R_{00}$ the time-time component of the Ricci tensor at $z$, $P_{\ln}\approx -0.84961$ is a numerical constant, and $\omega_\Lambda$ is the state's Hadamard coefficient $w_0(x,x')$ smeared by the probe. The first curvature term is purely geometric, so at leading order all Hadamard states agree; the state enters only through the constant $\omega_\Lambda$. The $R_{00}$ dependence reflects the chosen time direction of the Riemann normal coordinates, matching the fact that the Gaussian probe is not Lorentz invariant. The authors then show that a gapless Unruh-DeWitt detector interacting linearly with the field has a final state determined entirely by $\xi = \lambda^2\langle\hat\phi(\Lambda)^2\rangle_\omega$, so the geometric correction transfers directly: the curvature-induced change to the detector's final state is $\lambda^2 R(\Lambda)(\hat\rho_{d,0} + \hat\mu\hat\rho_{d,0}\hat\mu) + O(\ell^3)$, with $R(\Lambda)$ collecting the same geometric and state terms.

Load-bearing premise

The load-bearing premise is that the probe region is small compared with both the local curvature radius and the scale over which the state's Hadamard coefficient $w_0(x,x')$ varies, so that the smeared state contribution $\omega_\Lambda$ is a constant to leading order and the $O(\ell^2\ln\ell)$ remainder is genuinely subleading; if the state varies on scales comparable to $\ell$, the clean split between geometry and state fails, and the hard cutoff of the Gaussian tail required for compact support also enters the error estimates.

Editorial extensions

If this is right

  • A small probe of vacuum fluctuations directly measures a combination of the Ricci scalar and one Ricci component: subtracting the flat-space $1/(16\pi^2\ell^2)$ term from the measured variance leaves $- (5R+3R_{00})/(576\pi^2)$ plus the geometric log term, readable as a length-independent offset.
  • State dependence is reduced to a constant at leading order, so the geometric correction is universal: two different Hadamard states probing the same small region differ only through $\omega_\Lambda$, with state variation entering only at $O(\ell^2\ln\ell)$.
  • For gapless Unruh-DeWitt detectors, the final state is entirely a function of $\xi = \lambda^2\langle\hat\phi(\Lambda)^2\rangle_\omega$, so the curvature correction appears directly as a $\lambda^2 R(\Lambda)$ term in the detector's density matrix.
  • Replacing $\Lambda(x)\Lambda(x')$ with $\Lambda_-(x)\Lambda_+(x')$ in the same coefficient integrals yields the leading-order curvature correction to the excitation probability of a gapped particle detector.
  • Varying the probe size and orientation separates the contributions of $R$, $R_{00}$, and the Riemann tensor components, giving a concrete route to reconstructing local geometric data from field-fluctuation statistics.

Reading between the lines

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

  • Because the curvature correction is order $\ell^0$ while state-variation corrections are $O(\ell^2\ln\ell)$, shrinking the probe sharpens the universality claim: after subtracting the flat-space divergence, the leading residual is dominated by geometry plus the state constant, making different Hadamard states nearly indistinguishable at leading order.
  • The $R_{00}$ dependence means the measured correction depends on the time direction chosen for the Riemann normal coordinates; a natural testable extension is to compute the variance for a boosted or anisotropic Gaussian probe, where the appendix's general $T \neq \sigma$ expressions predict the full tensor structure coupling $R_{00}$, $R^i{}_i$, $R_{0i0j}$, and $R_{ijij}$.
  • The paper's explicit exclusion of delta-coupled detectors, which require Fermi normal coordinates and pick up trajectory acceleration and redshift effects, suggests a probe-size dichotomy: finite-size probes see the purely local geometric term, while instantaneous probes see trajectory-dependent geometry, and comparing the two in the same spacetime could isolate which geometric information each pr
  • A direct numerical test is within reach: compute the smeared variance exactly in a concrete spacetime with a known Hadamard state, such as de Sitter space in the Bunch-Davies vacuum, and check the $\ell \to 0$ residual against Eq. (38).
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper computes the leading-order curvature corrections to the expected value of the squared amplitude of a massless real scalar field smeared over a small spacetime region, using Riemann normal coordinates and the Hadamard form of the Wightman function. The central result, Eq. (38), separates a purely geometric correction proportional to R and R00 from a state-dependent constant ωΛ. The authors then apply this result to gapless Unruh-DeWitt detectors, obtaining the leading curvature correction to the detector's final state. Appendix A evaluates the geometric coefficients for a Gaussian spacetime smearing, and Appendix B derives the world-function expansion in Riemann normal coordinates.

Significance. If the final formula is correct, the paper gives an operational, parameter-free separation of geometry and state in a local field observable, with a concrete prediction for gapless detector response. The approach is analytic and does not fit any free parameter; the state term is honestly left undetermined, and the detector application is explicit. These are real strengths. However, the derivation as written contains a sign inconsistency in the chain from the world-function expansion to the smeared curvature correction, and the final coefficient in Eq. (38) depends on which sign is correct. The central claim is therefore not yet reliably established from the manuscript as it stands.

major comments (2)
  1. [Section III, Eqs. (32), (35), (36); Appendix B] There is a direct sign inconsistency between Eq. (32) and Eq. (35). Using the standard Riemann symmetries, R_acbd x^a x^b x'^c x'^d = -R_abcd x^a x^d x'^b x'^c. Therefore the smeared correction implied by Eq. (32) is +(4π²/3) R_abcd L_abcd, not the -(4π²/3) R_abcd L_abcd written in Eq. (35). If instead the sign in Eq. (B13) is the error, then Eq. (32) should have the opposite sign and Eq. (35) would be recovered. Either way, the manuscript as written is internally inconsistent, and the coefficient in Eq. (38) is not a valid consequence of the displayed derivation. The authors must fix the signs and re-derive Eqs. (37), (38), (46), and (47), as well as the corresponding expressions in Appendix A.
  2. [Section III, footnote 3; Appendix A] The Gaussian smearing in Eq. (14) is not compactly supported, and footnote 3 acknowledges that a hard cutoff is needed to define Λ as a compactly supported test function. However, all integrals in Appendix A and the value of P_ln are computed with the full Gaussian over R^4. The error introduced by the cutoff is not shown to be O(ℓ² ln ℓ), and because Riemann normal coordinates exist only in a normal neighbourhood, this is not a purely cosmetic point for the claimed asymptotic expansion. Please either justify that the cutoff corrections are beyond the truncation order or state the result directly for a Schwartz smearing without claiming compact support.
minor comments (4)
  1. [Section II, Eq. (10)] The variance is written as ⟨Δφ(Λ)⟩ω, but for a quasifree state this vanishes; the intended object is ⟨(Δφ(Λ))²⟩ω, and the notation should be corrected.
  2. [Section III, after Eq. (36)] The numerical value P_ln ≈ −0.84961 is given without specifying the integration method or providing code; this value should be reproducible from the text, so please include the evaluation procedure or an ancillary file.
  3. [Section IV, Eq. (47)] Eq. (47) contains a term ω0PΛ, but Eq. (36) defines only Pln and ωΛ; the symbol PΛ is not defined. Please clarify whether this is a typo for ωΛ or define PΛ explicitly.
  4. [Section II, paragraph after Eq. (14)] The text says 'an advantage of considering Λ(x) as given in Eq. (12)', but the Gaussian is defined in Eq. (14); the cross-reference should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the curvature corrections are derived from standard Hadamard and Riemann-normal-coordinate expansions, not from a fit or self-citation.

full rationale

The paper's central result, Eq. (38), is obtained by inserting the Hadamard form of the Wightman function (Eq. (20)) into the smeared expectation value (Eq. (18)), expanding Synge's world function in Riemann normal coordinates (Eq. (29)) and the metric determinant (Eq. (34)), and evaluating the resulting coefficient integrals in Appendix A for a Gaussian smearing. The geometric inputs—the Van Vleck expansion (Eq. (26)), the v0 = R/12 coefficient (Eq. (27)), and the RNC metric expansion (Eq. (B2))—are taken from standard external references (Poisson, DeWitt-Brehme), not from the authors' prior work. The state-dependent Hadamard coefficient w0 enters only through the explicitly undetermined constant ωΛ, which is honestly separated rather than fitted to force the curvature terms. No parameter is fitted and no closely related quantity is predicted from a subset of data. The self-citations that appear ([24], [53], [54], [58], [66]) are contextual or comparative: in particular, [66] is cited only to note that the present Gaussian-smearing expansion differs from the delta-coupled calculation of that paper (footnote 7), and the main derivation does not rely on any of these works. Any sign inconsistency between Eqs. (32) and (35) would be a correctness concern, not a circularity, because the claimed reduction would still be an independent computation. The derivation is therefore self-contained against external benchmarks and exhibits no circular step.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The derivation adds no new entities. The free parameters are the renormalization scale ℓ0 (absorbed into the state term) and the state-dependent constant ωΛ, which is not computed. The load-bearing assumptions are the Hadamard condition and the slow variation of w0, plus the compact-support cutoff for the Gaussian.

free parameters (2)
  • ℓ0 = ℓ (set equal to the probe size)
    Arbitrary renormalization scale in the Hadamard parametrix; the paper notes changes in ℓ0 are absorbed into w0. It is not fitted to data, but it does affect the numerical value of P_ln.
  • ωΛ = not computed
    The smeared state-dependent Hadamard coefficient w0. It is left as an undetermined constant, effectively a free parameter of the final formula for any specific state.
assumptions (5)
  • domain assumption The quantum state is quasifree and satisfies the Hadamard condition.
    Invoked in Section III to write the Wightman function in the Hadamard form (Eq. (20)); all subsequent expansions rely on this.
  • domain assumption The probe region lies inside the normal neighborhood of the central event z, so Riemann normal coordinates cover the support of Λ.
    Stated in Section III; the comparison of curved and flat smearings via RNC requires the support to be within the normal neighborhood.
  • domain assumption The smooth part w0(x,x') of the Hadamard parametrix varies slowly over the probe and contributes only a constant to leading order.
    Used after Eq. (36) to treat ωΛ as a leading-order constant; this is the key structural assumption for separating geometric from state effects.
  • ad hoc to paper The Gaussian smearing is effectively compactly supported by a hard cutoff.
    Acknowledged in footnote 3: the Gaussian in Eq. (14) is not compactly supported, so a cutoff is needed to define Λ(x) on the curved manifold; the error terms O(ℓ^2 ln ℓ) rely on this.
  • standard math Standard expansions of the Van Vleck determinant, v0, and √-g in Riemann normal coordinates.
    Quoted from [20] and [28] (Eqs. (26), (27), (34)); these are established results in the literature.

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Pith. "Pith review of The effect of curvature on local observables in quantum field theory." pith.science (2026). https://pith.science/paper/I4DZ2W6A

@misc{pith2026241212294,
  author       = {Pith},
  title        = {Pith review of: The effect of curvature on local observables in quantum field theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I4DZ2W6A}},
  note         = {Machine review of arXiv:2412.12294}
}
read the original abstract

We compute the leading order corrections to the expected value of the squared field amplitude of a massless real scalar quantum field due to curvature in a localized region of spacetime. We use Riemann normal coordinates to define localized field operators in a curved spacetime that are analogous to their flat space counterparts, and the Hadamard condition to find the leading order curvature corrections to the field correlations. We then apply our results to particle detector models, quantifying the effect of spacetime curvature in localized field probes.

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

80 extracted references · 59 canonical work pages

  1. [66]

    Mart ´ ın-Mart ´ ınez, T

    E. Mart ´ ın-Mart ´ ınez, T. R. Perche, and B. d. S. L. Torres, Broken covariance of particle de- tector models in relativistic quantum information, Phys. Rev. D 103, 025007 (2021)

    work page 2021

  2. [1]

    Parker, Quantized fields and particle creation in ex- panding universes

    L. Parker, Quantized fields and particle creation in ex- panding universes. i, Phys. Rev. 183, 1057 (1969)

    work page 1969

  3. [2]

    Agullo and L

    I. Agullo and L. Parker, Non-gaussianities and the stim- ulated creation of quanta in the inflationary universe, Phys. Rev. D 83, 063526 (2011)

    work page 2011

  4. [3]

    This ensures that the spacetime support of Λ( x) behaves in the same way in which the support of Λ 0(x) behaves in Minkowski spacetime, in the following sense. Given a region U in Minkowski spacetime, one can define its maximal geodesic size as ℓU ≡ sup x,x′∈U √ 2|σ(x, x′)|, (19) corresponding to the maximal spacetime separation be- tween any two events in...

    work page

  5. [4]

    S. W. Hawking, Particle creation by black holes, Communications in Mathematical Physics 43, 199 (1975)

    1975

  6. [5]

    G. W. Gibbons and S. W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15, 2738 (1977)

    1977

  7. [6]

    How- ever, in this case L cannot be interpreted as an excita- tion probability, as the detector does not have an energy gap

    becomes proportional to ⟨ˆφ(Λ) ⟩ω. How- ever, in this case L cannot be interpreted as an excita- tion probability, as the detector does not have an energy gap. Gapless detectors have been studied in detail [ 56– 58], partially because their interaction with the field can be solved non-perturbatively, but also for their ability to describe degenerate subsys...

    work page

  8. [7]

    S. A. Fulling, F. J. Narcowich, and R. M. Wald, Singularity Structure of the Two Point Function in Quantum Field Theory in Curved Space-time. II, Annals Phys. 136, 243 (1981)

    work page 1981

Show all 80 references
  1. [8]

    B. S. Kay and R. M. Wald, Theorems on the unique- ness and thermal properties of stationary, nonsingular, quasifree states on spacetimes with a bifurcate killing horizon, Phys. Rep. 207, 49 (1991)

    1991

  2. [9]

    D´ ecanini and A

    Y. D´ ecanini and A. Folacci, Hadamard renormaliza- tion of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension, Phys. Rev. D 78, 044025 (2008)

    2008

  3. [10]

    due to the Riemann and Ricci tensors. The first correction is − 1 12 RabLab = − T 2R00 + σ2 ∑ 3 i=1 Rii 48π2(T 2 + σ2) , (A15) whereas the coupling with the Riemann tensor yields − 4π2 3 RabcdLabcd = − 4π2 3 Rabcd ˜Labcd (A16) = − 4π2 3 R0i0j ( ˜L0i0j − ˜Li00j − ˜L0ij0) − 4π2 3...

  4. [11]

    (A19) In particular, by setting σ = T one obtains − 4π2 3 RabcdLabcd − 1 12 RabLab (A20) = 2R00 − 5Ri i 576π2 = − 5R + 3R00 576π2

    due to the Ricci and Riemann tensors take the form − 1 12 RabLab − 4π2 3 RabcdLabcd = −3T 6 − 4T 4σ2 + 6T 2σ4 + 5σ6 144π2 (T 2 + σ2)3 R00 − 3T 2σ2 + 2σ4 144π2 (T 2 + σ2)2 Ri i. (A19) In particular, by setting σ = T one obtains − 4π2 3 RabcdLabcd − 1 12 RabLab (A20) = 2R00 − 5R...

  5. [12]

    (B8) Combining this expression with the symmetries of the Riemann tensor, we get ∂bΓ a cd(z) = − 1 3 (Ra cdb(z) + Ra dcb(z))

    (B7) Now, because the point z is the centre of the RNC system, we can write Ra bcd(z) = ∂cΓ a bd(z) − ∂dΓ a bc(z). (B8) Combining this expression with the symmetries of the Riemann tensor, we get ∂bΓ a cd(z) = − 1 3 (Ra cdb(z) + Ra dcb(z)). (B9) Then, the expansion of the geod...

  6. [13]

    T. R. Perche, J. Polo-G´ omez, B. d. S. L. Torres, and E. Mart ´ ın-Mart ´ ınez, Particle de- tectors from localized quantum field theories, Phys. Rev. D 109, 045013 (2024)

    2024

  7. [14]

    is not Lorentz invariant. IV. EFFECTIVE PROBES OF QUANTUM FIELDS In this section we will discuss how to physically ac- cess the smeared field operators of the form ˆφ(Λ), utiliz- ing local probes in quantum field theory. As we previ- ously mentioned, the spacetime smearing funct...

  8. [15]

    S. W. Hawking, Black hole explosions, Nature 248, 30 (1974)

    1974

  9. [16]

    Haag, Local Quantum Physics: Fields, Particles, Al- gebras, 1st ed

    R. Haag, Local Quantum Physics: Fields, Particles, Al- gebras, 1st ed. (Springer Publishing Company, Incorpo- rated, 2012)

    2012

  10. [17]

    Araki, Mathematical Theory of Quantum Fields , In- ternational series of monographs on physics (Oxford Uni- versity Press, 1999)

    H. Araki, Mathematical Theory of Quantum Fields , In- ternational series of monographs on physics (Oxford Uni- versity Press, 1999)

    1999

  11. [18]

    Essentially, for x, x′ within this region, we have σ(x, x′) = O(ℓ2)

    in Riemann normal coordinates (RNC), which will also allow us to perform an expansion in ℓ, that is, an expansion in the effective size of the region that local- izes the observable ˆφ(Λ) 2. Essentially, for x, x′ within this region, we have σ(x, x′) = O(ℓ2). The Riemann normal...

  12. [19]

    S. A. Fulling, M. Sweeny, and R. M. Wald, Singularity structure of the two-point function in quantum field theory in curved spacetime, Commun. Math. Phys 63, 257 (1978)

    1978

  13. [20]

    Poisson, The motion of point particles in curved space- time, Living Rev

    E. Poisson, The motion of point particles in curved space- time, Living Rev. Relativ. 7, 10.12942/lrr-2004-6 (2004)

    2004 doi

  14. [21]

    G. C. Wick, The evaluation of the collision matrix, Phys. Rev. 80, 268 (1950)

    1950

  15. [22]

    (27) Combining these results, we can recast the Wightman function as W (x, x′) = Wσ(x, x′) ( 1 + 1 12 Rαβ(x)σασβ ) (28) + 1 12 R(x)ln ( σ/ℓ2 0 ) + w0(x, x′) + O(σ ln σ)

    can also be expanded as [ 28] v0(x, x′) = R(x) 12 + O(σ). (27) Combining these results, we can recast the Wightman function as W (x, x′) = Wσ(x, x′) ( 1 + 1 12 Rαβ(x)σασβ ) (28) + 1 12 R(x)ln ( σ/ℓ2 0 ) + w0(x, x′) + O(σ ln σ). Our goal is now to write the integral that defines...

  16. [23]

    C. J. Fewster and R. Verch, The ne- cessity of the hadamard condition, Class. Quantum Grav. 30, 235027 (2013)

    2013

  17. [24]

    C. J. Fewster, A generally covariant measurement scheme for quantum field theory in curved spacetimes, in Progress and Visions in Quantum Theory in View of Gravity 11 (Springer International Publishing, 2020) pp. 253–268

    2020

  18. [25]

    Polo-G´ omez, L

    J. Polo-G´ omez, L. J. Garay, and E. Mart ´ ın-Mart ´ ınez, A detector-based measurement theory for quantum field theory, Phys. Rev. D 105, 065003 (2022)

    2022

  19. [26]

    W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D 14, 870 (1976)

    1976

  20. [27]

    DeWitt, General Relativity; an Einstein Centenary Survey (Cambridge University Press, Cambridge, UK, 1980)

    B. DeWitt, General Relativity; an Einstein Centenary Survey (Cambridge University Press, Cambridge, UK, 1980)

    1980

  21. [28]

    B. S. DeWitt and R. W. Brehme, Radiation damping in a gravitational field, Annals of Physics 9, 220 (1960)

    1960

  22. [29]

    W. G. Unruh and R. M. Wald, What happens when an accelerating observer detects a rindler particle, Phys. Rev. D 29, 1047 (1984)

    1984

  23. [30]

    Fewster and K

    C. Fewster and K. Rejzner, Algebraic quantum field the- ory: An introduction, in Progress and Visions in Quan- tum Theory in View of Gravity , edited by F. Finster, D. Giulini, J. Kleiner, and J. Tolksdorf (Birkhauser, 2020)

    2020

  24. [31]

    Khavkine and V

    I. Khavkine and V. Moretti, Algebraic qft in curved spacetime and quasifree hadamard states: An introduc- tion, in Advances in Algebraic Quantum Field Theory (Springer International Publishing, 2015) p. 191–251

    2015

  25. [32]

    Silman and B

    J. Silman and B. Reznik, Long-range entanglement in the Dirac vacuum, Phys. Rev. A 75, 052307 (2007)

    2007

  26. [33]

    Salton, R

    G. Salton, R. B. Mann, and N. C. Menicucci, Acceleration-assisted entanglement harvesting and rangefinding, New J. Phys. 17, 035001 (2015)

    2015

  27. [34]

    Saravani, S

    M. Saravani, S. Aslanbeigi, and A. Kempf, Space- time curvature in terms of scalar field propagators, Phys. Rev. D 93, 045026 (2016)

    2016

  28. [35]

    in our expression for the final state of the detector in ( 45), we can also find the leading or- der corrections to the final state of the detector due to curvature in a region of size ℓ, namely ˆρd = e−ξ0 cosh(ξ0)ˆρd,0 + e−ξ0 sinh(ξ0)ˆµˆρd,0 ˆµ (46) + λ2R(Λ)(ˆρd,0 + ˆµˆρd,0 ˆµ) ...

  29. [36]

    in the short distance limit. To this end, we shall work with a Gaussian spacetime smearing prescribed in RNC, namely Λ( x) = Λ( t, x) = e− −t2 2T 2 √ 2πT e− |x|2 2σ 2 (2πσ2)3/2 , (A1) where we employed the notation xa = (t, x) for the RNC system centered at z. For this specific...

  30. [37]

    Kempf, Replacing the notion of space- time distance by the notion of correlation, Frontiers in Physics 9, 247 (2021)

    A. Kempf, Replacing the notion of space- time distance by the notion of correlation, Frontiers in Physics 9, 247 (2021)

    2021

  31. [38]

    T. R. Perche and E. Mart ´ ın-Mart ´ ınez, Geom- etry of spacetime from quantum measurements, Phys. Rev. D 105, 066011 (2022)

    2022

  32. [39]

    N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space , Cambridge Mono- graphs on Mathematical Physics (Cambridge University Press, 1982)

    1982

  33. [40]

    Synge, A characteristic function in Riemannian space and its applications to the solution of geodesic triangles, Proc

    J. Synge, A characteristic function in Riemannian space and its applications to the solution of geodesic triangles, Proc. Lond. Math. Soc. 32, 241 (1931)

    1931

  34. [41]

    J. H. Van Vleck, The correspondence principle in the statistical interpretation of quantum mechanics, Proc Natl Acad Sci U S A 14, 178 (1928)

    1928

  35. [42]

    Also notice that if Ω = 0, Λ +(x) = Λ −(x) = Λ( x), and Eq

    samples frequencies of the correlation function that effectively resonate with the detector’s energy gap. Also notice that if Ω = 0, Λ +(x) = Λ −(x) = Λ( x), and Eq. (

  36. [43]

    Valentini, Non-local correlations in quantum electro- dynamics, Phys

    A. Valentini, Non-local correlations in quantum electro- dynamics, Phys. Lett. A 153, 321 (1991)

    1991

  37. [44]

    Reznik, A

    B. Reznik, A. Retzker, and J. Silman, Violating bell’s inequalities in vacuum, Phys. Rev. A 71, 042104 (2005)

    2005

  38. [45]

    Funai and E

    N. Funai and E. Mart ´ ın-Mart ´ ınez, Engineering negative stress-energy densities with quantum energy teleporta- tion, Phys. Rev. D 96, 025014 (2017)

    2017

  39. [46]

    Pozas-Kerstjens and E

    A. Pozas-Kerstjens and E. Mart ´ ın-Mart ´ ınez, Har- vesting correlations from the quantum vacuum, Phys. Rev. D 92, 064042 (2015)

    2015

  40. [47]

    Pozas-Kerstjens and E

    A. Pozas-Kerstjens and E. Mart ´ ın-Mart ´ ınez, Entangle- ment harvesting from the electromagnetic vacuum with hydrogenlike atoms, Phys. Rev. D 94, 064074 (2016)

    2016

  41. [48]

    in Riemann nor- mal coordinates. Indeed, in [ 66] a similar expansion to that of Section ( III) was performed 7, where the leading order effect of curvature in the excitation probability of delta coupled detectors was obtained using Fermi normal coordinates. The expansions of [...

  42. [49]

    L. J. Henderson and N. C. Menicucci, Bandlimited entan- glement harvesting, Phys. Rev. D 102, 125026 (2020)

    2020

  43. [50]

    M. P. G. Robbins, L. J. Henderson, and R. B. Mann, Entanglement amplification from rotating black holes, Class. Quantum Gravity 39, 02LT01 (2021)

    2021

  44. [51]

    Mendez-Avalos, L

    D. Mendez-Avalos, L. J. Henderson, K. Gallock- Yoshimura, and R. B. Mann, Entanglement harvesting of three Unruh-DeWitt detectors, Gen. Relativ. and Gravit. 54, 87 (2022)

    2022

  45. [52]

    Tjoa and E

    E. Tjoa and E. Mart ´ ın-Mart ´ ınez, When entangle- ment harvesting is not really harvesting (2021), arXiv:2109.11561 [quant-ph]

    2021 arXiv

  46. [53]

    T. R. Perche, C. Lima, and E. Mart ´ ın-Mart ´ ınez, Harvesting entanglement from complex scalar and fermionic fields with linearly coupled particle detectors, Phys. Rev. D 105, 065016 (2022)

    2022

  47. [54]

    T. R. Perche, B. Ragula, and E. Mart ´ ın-Mart ´ ınez, Har- vesting entanglement from the gravitational vacuum, Phys. Rev. D 108, 085025 (2023)

    2023

  48. [55]

    M. H. Zambianco, A. Teixid´ o-Bonfill, and E. Mart ´ ın- Mart ´ ınez, Interference of communication and field correlations in entanglement harvesting, Phys. Rev. D 110, 025016 (2024)

    2024

  49. [56]

    Hotta, J

    M. Hotta, J. Matsumoto, and G. Yusa, Quantum energy teleportation without a limit of distance, Phys. Rev. A 89, 012311 (2014)

    2014

  50. [57]

    Hotta, Quantum measurement information as a key to energy extraction from local vacuums, Phys

    M. Hotta, Quantum measurement information as a key to energy extraction from local vacuums, Phys. Rev. D 78, 045006 (2008)

    2008

  51. [58]

    N. A. Rodr ´ ıguez-Briones, H. Katiyar, E. Mart ´ ın- Mart ´ ınez, and R. Laflamme, Experimental activation of strong local passive states with quantum information, Phys. Rev. Lett. 130, 110801 (2023)

    2023

  52. [59]

    R. H. Jonsson, E. Mart ´ ın-Mart ´ ınez, and A. Kempf, Information transmission without energy exchange, Phys. Rev. Lett. 114, 110505 (2015)

    2015

  53. [60]

    Blasco, L

    A. Blasco, L. J. Garay, M. Mart ´ ın-Benito, and E. Mart ´ ın- Mart ´ ınez, Timelike information broadcasting in cosmol- ogy, Phys. Rev. D 93, 024055 (2016)

    2016

  54. [61]

    Blasco, L

    A. Blasco, L. J. Garay, M. Mart ´ ın-Benito, and E. Mart ´ ın- Mart ´ ınez, Violation of the strong huygen’s princi- ple and timelike signals from the early universe, Phys. Rev. Lett. 114, 141103 (2015)

    2015

  55. [62]

    Simidzija, A

    P. Simidzija, A. Ahmadzadegan, A. Kempf, and E. Mart ´ ın-Mart ´ ınez, Transmission of quan- tum information through quantum fields, Phys. Rev. D 101, 036014 (2020)

    2020

  56. [63]

    Yamaguchi, A

    K. Yamaguchi, A. Ahmadzadegan, P. Simidzija, A. Kempf, and E. Mart ´ ın-Mart ´ ınez, Superadditiv- ity of channel capacity through quantum fields, Phys. Rev. D 101, 105009 (2020)

    2020

  57. [64]

    Yamaguchi and A

    K. Yamaguchi and A. Kempf, Entangle- ment is better teleported than transmitted, Phys. Rev. D 108, 025004 (2023) . 12

    2023

  58. [65]

    Mart ´ ın-Mart ´ ınez, T

    E. Mart ´ ın-Mart ´ ınez, T. R. Perche, and B. de S. L. Tor- res, General relativistic quantum optics: Finite- size particle detector models in curved spacetimes, Phys. Rev. D 101, 045017 (2020)

    2020

  59. [67]

    T. R. Perche, Localized nonrelativistic quantum systems in curved spacetimes: A general characterization of par- ticle detector models, Phys. Rev. D 106, 025018 (2022)

    2022

  60. [68]

    A. G. S. Landulfo, Nonperturbative approach to relativistic quantum communication channels, Phys. Rev. D 93, 104019 (2016)

    2016

  61. [69]

    Pozas-Kerstjens, J

    A. Pozas-Kerstjens, J. Louko, and E. Mart ´ ın-Mart ´ ınez, Degenerate detectors are unable to harvest spacelike en- tanglement, Phys. Rev. D 95, 105009 (2017)

    2017

  62. [70]

    T. R. Perche, Closed-form expressions for smeared bidis- tributions of a massless scalar field: Nonperturbative and asymptotic results in relativistic quantum information, Phys. Rev. D 110, 025013 (2024)

    2024

  63. [71]

    Magnus, On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7, 649 (1954)

    W. Magnus, On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7, 649 (1954)

    1954

  64. [72]

    Blanes, F

    S. Blanes, F. Casas, J. Oteo, and J. Ros, The magnus expansion and some of its applications, Physics Reports 470, 151 (2009)

    2009

  65. [73]

    H. K and D. Kothawala, Effect of tidal cur- vature on dynamics of accelerated probes, Phys. Rev. D 104, 064032 (2021)

    2021

  66. [74]

    H. K, S. Barman, and D. Kothawala, Univer- sal role of curvature in vacuum entanglement, Phys. Rev. D 109, 065017 (2024)

    2024

  67. [75]

    H. K and D. Kothawala, Rotating detectors in ds and ads spacetimes, Phys. Rev. D 109, 104073 (2024)

    2024

  68. [76]

    Simidzija and E

    P. Simidzija and E. Mart ´ ın-Mart ´ ınez, Nonperturbative analysis of entanglement harvesting from coherent field states, Phys. Rev. D 96, 065008 (2017)

    2017

  69. [77]

    Simidzija, R

    P. Simidzija, R. H. Jonsson, and E. Mart ´ ın-Mart ´ ınez, General no-go theorem for entanglement extraction, Phys. Rev. D 97, 125002 (2018)

    2018

  70. [78]

    T. R. Perche and A. Shalabi, Spacetime curva- ture from ultrarapid measurements of quantum fields, Phys. Rev. D 105, 125011 (2022)

    2022

  71. [79]

    Shalabi, L

    A. Shalabi, L. J. Henderson, and R. B. Mann, Locally detecting uv cutoffs on a sphere with particle detectors, Phys. Rev. D 107, 045006 (2023)

    2023

  72. [80]

    Tjoa, Nonperturbative simple-generated interactions with a quantum field for arbitrary gaussian states, Phys

    E. Tjoa, Nonperturbative simple-generated interactions with a quantum field for arbitrary gaussian states, Phys. Rev. D 108, 045003 (2023)

    2023

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