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REVIEW 2 major objections 3 minor 71 references

Quantum Fisher information of a cosmic qubit undergoing non-Markovian de Sitter evolution

T0 review · 2 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Non-Markovian memory cuts precision of cosmic Hubble estimates

desk verdict The non-Markovian master-equation solution is real and carefully done, but the QFI analysis uses an invalid qubit formula, so the paper's headline metrology claims are unsupported. read the letter →

arxiv 2411.11490 v3 pith:HHRC7STF submitted 2024-11-18 hep-th

Langxuan Chen , Jun Feng This is my paper · ORCID
classification hep-th
keywords Unruh-DeWittdetectordeSitterspacealpha-vacuanon-MarkoviandynamicsquantumFisherinformationHubbleparameterestimationopensystemsGibbons-Hawkingeffect
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

An Unruh-DeWitt detector, a two-level quantum system coupled to a background scalar field, is a standard probe of quantum fields in curved spacetime. This paper derives its full evolution in de Sitter space without the usual Markov and rotating-wave approximations, keeping the memory effects of the field, and then uses quantum Fisher information (QFI) to ask how precisely the Hubble parameter $H$ can be estimated from the detector's state. The central finding is that the non-Markovian, memoryful dynamics generally make $H$ harder to estimate than the Markovian approximation suggests: the QFI is lower throughout the evolution, nearly vanishes at early times where the Markovian solution shows linear growth, and at late times converges to an asymptotic value independent of the detector's initial state. For the one-parameter family of $\alpha$-vacua, that asymptotic QFI is significantly suppressed relative to the Bunch-Davies vacuum, and it vanishes as $\alpha \to 0^-$ because the equilibrium state becomes $H$-independent. This matters because it sets a realistic ceiling on Hubble-parameter metrology with cosmic qubits and exposes where the common Markovian approximation overstates sensitivity.

What carries the argument

The central object is the exact non-Markovian detector state obtained from the Laplace-resolved master equation. Starting from the integro-differential master equation (2.6) (Born approximation only, no Markov or rotating-wave approximation), the paper Laplace-transforms in time and identifies two classes of poles: Markovian poles near $z=0$ that give exponential decay with rates $\Gamma_{(0)}$, $\Gamma_{(\pm)}$, and infinite sequences of non-Markovian poles near $z=-nH\pm i\omega$ (and $z=-nH$) whose residues produce the correction functions $S_{(0)}(\tau)$ and $S_{(\pm)}(\tau)$. The detector Bloch vector is then expressed in terms of these decay rates and correction functions, with the frequency renormalized to the physical $\Omega$ and the state renormalized at proper time $\kappa$. Feeding this solution into the two-level QFI formula (3.7) yields the claimed reduction: the $S$-corrections shrink the Bloch vector's coherence and lower the QFI throughout the evolution. The $\alpha$-vacua, a one-parameter family of de Sitter-invariant vacua labeled by $\alpha<0$ and realized as squeezed states over the Bunch-Davies vacuum ($\alpha\to-\infty$), enter through the Wightman function and through the coefficients $\gamma_{(0)}$, $\Gamma_{(0)}$, and $\Gamma_{(\pm)}$, which determine the $H$-independent equilibrium state whose $\alpha$-dependence suppresses the late-time QFI.

What would settle it

Compute the same asymptotic QFI for renormalization times $\kappa H = 10^{-4}, 10^{-3}, 10^{-2}$ and cutoffs $\epsilon = 10^{-2}, 10^{-3}, 10^{-4}$; if the claimed reduction and $\alpha$-suppression do not remain approximately fixed, the central claim is an artifact of the chosen $\kappa$. An alternative direct test is numerical integration of the integro-differential master equation (2.6) with the $\alpha$-vacuum Wightman function and comparison of the resulting QFI with the residue-based solution (2.75).

Watch

Extended reading notes

Core claim

The paper claims that the exact non-Markovian evolution of a comoving Unruh-DeWitt detector in (3+1)-dimensional de Sitter space reduces the quantum Fisher information for the Hubble parameter compared with the Markovian-approximated evolution, and that for general $\alpha$-vacua the reduction is stronger. Concretely, the detector density matrix is solved through a Laplace-transformed integro-differential master equation, giving Bloch coefficients $v_{(0)}(\tau)$ and $v_{(\pm)}(\tau)$ as sums of Markovian pole contributions (exponential decay with rates $\Gamma_{(0)}$, $\Gamma_{(\pm)}$) and non-Markovian pole contributions involving Lerch transcendents. After renormalizing at a proper time $\kappa$, the authors insert this solution into the qubit QFI formula and find that the non-Markovian contributions lower the QFI relative to the Markovian solution at all times, that for $H\tau \lesssim 1$ the exact QFI remains nearly zero while the Markovian QFI grows linearly, and that at late times all initial states converge to the same asymptotic QFI. For $\alpha$-vacua other than Bunch-Davies, the asymptotic value is suppressed, eventually vanishing as $\alpha \to 0^-$ because the equilibrium state approaches the $H$-independent identity density matrix; the paper interprets the $\alpha$-dependent large-$\Omega$ equilibrium state as evidence for the infinite-energy pathology of non-Bunch-Davies vacua.

Load-bearing premise

The physical conclusion depends on the renormalization of the detector state at an arbitrary proper time $\kappa$ (numerically $\kappa H=10^{-3}$) being $\kappa$-independent, which the paper does not demonstrate; it also depends on assuming a tiny nonzero mass for the scalar field to define the de Sitter vacuum, a choice incompatible with the Markovian limit it compares against.

Editorial extensions

If this is right

  • Hubble-parameter estimation from a comoving qubit in de Sitter space is less precise under exact non-Markovian dynamics than Markovian calculations suggest, at all times of the evolution.
  • At late times the QFI converges to an asymptotic value independent of the detector's initial state, confirming that the detector reaches a unique equilibrium state whose $H$-dependence controls the achievable estimation precision.
  • For very small or very large detector energy gaps the asymptotic QFI vanishes, because the equilibrium state becomes independent of $H$, so only a fine-tuned detector gap yields a useful Hubble measurement.
  • For any deviation from the Bunch-Davies vacuum, the asymptotic QFI is suppressed, and as $\alpha\to0^-$ the equilibrium state approaches the $H$-independent identity state, making Hubble estimation impossible.
  • The non-Markovian effects reshuffle the effective initial conditions of the detector at late times, reducing its coherence and therefore its QFI relative to the Markovian path.

Reading between the lines

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

  • Editorial inference: the renormalization at an arbitrary proper time $\kappa$ (all numerics use $\kappa H=10^{-3}$) is not shown by the paper to be physically irrelevant; a scan over $\kappa$ would directly test whether the claimed reduction and suppression are conventions rather than robust features.
  • Editorial inference: the tiny-mass assumption needed to define a de Sitter-invariant vacuum already breaks the Markovian limit, so the Markovian-versus-non-Markovian comparison may mix genuine memory effects with a change of vacuum regularization.
  • Editorial inference: the same Laplace-transform and pole-residue machinery should transfer to black-hole or FRW backgrounds, where non-Markovian memory would likely also lower the QFI; the authors note this possibility but do not compute it.
  • Editorial inference: a direct numerical integration of the integro-differential master equation (2.6) with the $\alpha$-vacuum Wightman function would provide an independent check of the residue-based solution and of the $O(\epsilon\log\epsilon)$ estimates.
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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 / 3 minor

Summary. The paper derives the full non-Markovian, non-RWA dynamics of a comoving Unruh-DeWitt detector in (3+1)-dimensional de Sitter space for the one-parameter family of α-vacua, by Laplace-transforming the Born-approximated master equation, locating the pole structure of the transformed Bloch coefficients, and renormalizing the resulting divergences at a finite proper-time scale κ. It then uses quantum Fisher information (QFI) of the Hubble parameter as a process function, and claims that the non-Markovian contribution generally reduces the QFI relative to the Markovian solution, and that α-vacua significantly suppress the asymptotic QFI compared to the Bunch-Davies case. The central numerical evidence consists of early- and late-time QFI curves in Figs. 5–9, computed with g=0.1, H=2π, and κH=10^{-3}.

Significance. If the central claims were correct, the paper would be a useful contribution to relativistic quantum metrology and to the open-quantum-system treatment of UDW detectors, extending prior Markovian analyses to non-Markovian de Sitter evolution and connecting vacuum choices to metrological precision. The analytic derivation is substantial and largely self-contained: the Laplace-transform solution, residue calculus, renormalization appendix, and the explicit initial-condition checks around Eqs. (2.49)–(2.53) and Appendix D are careful and are not obtained by fitting parameters to produce the final suppression. The weakness is that the main quantitative conclusions are computed through Eq. (3.7), which is not the correct QFI for the complex Bloch parametrization actually used in the paper, so the headline claims are presently unsupported and need to be recomputed with the correct formula.

major comments (2)
  1. [§3.1, Eq. (3.7)] Equation (3.7) is not the QFI for the Bloch parametrization used in the paper. In Eqs. (2.11)–(2.12), v(0) is real but v(+) and v(−) are complex conjugates, so the physical Bloch vector is r=(√2 Re v_+, √2 Im v_+, v_0). The correct qubit QFI is F = (∂v_0)^2 + 2|∂v_+|^2 + [v_0 ∂v_0 + 2 Re(v_+ ∂v_+^*)]^2 / (1 − v_0^2 − 2|v_+|^2). Equation (3.7) instead contains (∂v_μ)^2 and (v_μ ∂v_μ)^2 without modulus or real-part operations; for the evolved state v_+(t)=v_+(0)e^{−Γ_+ t} with complex Γ_+, the sum in (3.7) is not even real. Every numerical QFI curve in Figs. 5–9, and with them the abstract's claims that non-Markovianity reduces QFI and that general α-vacua suppress the asymptotic QFI, is computed through this formula, so those conclusions are not supported in their present form. The authors should derive the QFI correctly for their parametrization and recompute the figures.
  2. [§2.5.2, Eq. (2.75), Figs. 5–9] The renormalization prescription fixes the detector state at an arbitrary proper time τ=κ and then sets ϵ=0, and all numerical results use κH=10^{-3}; the paper never demonstrates that the resulting QFI is independent of κ. The asymptotic state (2.69) is κ-independent, but the early-time behavior and the finite-time approach curves depend on κ through the terms S_μ(t+κ)−S_μ(κ) in Eq. (2.75), so the quantitative magnitude of the claimed QFI reduction at finite times could be an artifact of the chosen κ. Please either provide an analytic argument that F_Q(H;α) is κ-independent to the working order, or show numerically that varying κH over a range (for example 10^{-4} to 10^{-2}) leaves the QFI curves and the suppression claims unchanged.
minor comments (3)
  1. [References] References [50] and [67] are the same paper (Breuer, Laine, Piilo, and Vacchini, Rev. Mod. Phys. 88, 021002 (2016)) and should be merged or cross-referenced.
  2. [Figures 5–9] The line-type labels in the captions are inconsistent (for example, 'Dash-solid lines' in Figure 5); please clarify which line style corresponds to which solution and parameter set.
  3. [§2.3.1 and §2.3.2] The names 'Markovian poles' and 'non-Markovian poles' are potentially confusing because the latter also contribute to the Markov-approximated evolution in certain limits; a short explanatory sentence after Fig. 1 would help the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the QFI claims follow from an independently derived non-Markovian density matrix, not from a fitted or self-referential input.

full rationale

The paper's central claim—that non-Markovian evolution reduces QFI and that general α-vacua suppress the asymptotic QFI—is not circular. The detector state (2.56), (2.61), and the renormalized version (2.75) are obtained by Laplace transforming the exact integro-differential master equation (2.10), computing residues at Markovian and non-Markovian poles using the α-vacua Wightman functions (2.19)-(2.24), and imposing a finite-time renormalization condition at τ=κ. No parameter is fitted to the QFI values; the free parameters (g, ω, H, α, κ, initial state) enter as model inputs. The late-time QFI is a function of the derived equilibrium state (2.69)/(3.9)/(3.11), and the suppression with α follows algebraically from γ(0) in (2.48)/(2.74), not from any prior knowledge of the target result. Self-citations such as [45], [49], and [52] are used for background, standard formulas, or motivation; none is load-bearing for the main claim, and no uniqueness theorem from the authors' prior work is invoked to forbid alternatives. The 'shifted-Markovian' interpretation in (2.71)-(2.72) is a reformulation of the same solution rather than a separate prediction, so it does not make the argument circular. The skeptic concern that Eq. (3.7) is not the real QFI for a complex Bloch vector is a correctness objection to the numerical evaluation, not a reduction of the output to the input; this pass therefore records no circular step.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The derivation starts from the standard UDW interaction and the Born-approximated master equation (2.6). The only hand-chosen numerical parameter is the renormalization point κ, fixed in the plots. The α-vacua and their Wightman functions are taken from prior literature, not introduced ad hoc. No new entities are postulated.

free parameters (1)
  • κ (renormalization point) = κH = 10^-3 in all numerics
    Introduced in Section 2.5.2 as the time at which initial conditions are fixed; physical results are assumed independent of it, but no κ-independence check is provided.
assumptions (4)
  • domain assumption Born approximation and weak coupling (g small), so the master equation (2.6) is accurate to O(g^4); environment state satisfies [HΦ,ρΦ]=0 and ⟨ϕ⟩=0.
    Section 2.1; the entire derivation starts from (2.6), which is valid only in this regime.
  • domain assumption A de Sitter invariant vacuum exists for the background scalar field; for a massless field this is not strictly true, so a tiny mass is assumed (footnote 2), which in turn is said to break the Markovian limit.
    Section 2.2, footnote 2 explicitly flags this subtlety.
  • domain assumption The detector is comoving in planar coordinates of de Sitter space, and the interaction Hamiltonian has the specific form (2.2) with three Pauli couplings.
    Section 2.1 and 2.2; the results depend on this setup.
  • ad hoc to paper The renormalization prescription in Section 2.5.2: fixing initial conditions at arbitrary scale κ and setting ϵ=0 yields physical results independent of κ.
    No κ-independence check is provided; numerics fix κH=10^-3.

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Pith. "Pith review of Quantum Fisher information of a cosmic qubit undergoing non-Markovian de Sitter evolution." pith.science (2026). https://pith.science/paper/HHRC7STF

@misc{pith2026241111490,
  author       = {Pith},
  title        = {Pith review of: Quantum Fisher information of a cosmic qubit undergoing non-Markovian de Sitter evolution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HHRC7STF}},
  note         = {Machine review of arXiv:2411.11490}
}
abstract

We revisit the problem of thermalization process for an Unruh-DeWitt (UDW) detector in de Sitter space. We derive the full dynamics of the detector in the context of open quantum system, neither using Markovian or RWA approximations. We utilize quantum Fisher information (QFI) for Hubble parameter estimation, as a process function to distinguish the thermalization paths in detector Hilbert space, determined by its local properties, e.g., detector energy gap and its initial state preparation, or global spacetime geometry. We find that the non-Markovian contribution in general reduces the QFI comparing with Markovian approximated solution. Regarding to arbitrary initial states, the late-time QFI would converge to an asymptotic value. In particular, we are interested in the background field in the one parameter family of $\alpha$-vacua in de Sitter space. We show that for general $\alpha$-vacuum choices, the asymptotic values of converged QFI are significantly suppressed, comparing to previous known results for Bunch-Davies vacuum.

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Reference graph

Works this paper leans on

71 extracted references · 66 canonical work pages

  1. [1]

    Anninos, De Sitter musings , Int

    D. Anninos, De Sitter musings , Int. J. Mod. Phys. A 27, 1230013 (2012)

    work page 2012

  2. [2]

    Witten, Quantum Gravity In De Sitter Space , arXiv:hep-th/0106109

    E. Witten, Quantum Gravity In De Sitter Space , arXiv:hep-th/0106109

    arXiv

  3. [3]

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

    work page 1976

  4. [4]

    B. S. DeWitt, Quantum gravity: the new synthesis, in General Relativity: An Einstein Centenary Survey , edited by S.W. Hawking and W. Israel (Cambridge University Press, Cambridge, 1979), pp. 680

    work page 1979

  5. [5]

    N. D. Birrell and P. C. W. Davies, Quantum fields in curved space , Cambridge University Press (1982)

    work page 1982

  6. [6]

    L. C. B. Crispino, A. Higuchi and G. E. A. Matsas, The Unruh effect and its applications , Rev. Mod. Phys. 80, 787 (2008)

    work page 2008

  7. [7]

    Candelas, Vacuum polarization in Schwarzschild spacetime , Phys

    P. Candelas, Vacuum polarization in Schwarzschild spacetime , Phys. Rev. D 21, 2185 (1980)

    work page 1980

  8. [8]

    S. W. Hawking, Particle creation by black holes , Commun. Math. Phys. 43, 199 (1975)

    work page 1975

Show all 71 references
  1. [9]

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

    1977

  2. [10]

    Garbrecht and T

    B. Garbrecht and T. Prokopec, Unruh response functions for scalar fields in de Sitter space , Class. Quant. Grav. 21, 4993 (2004)

    2004

  3. [11]

    G. L. Sewell, Quantum fields on manifolds: PCT and gravitationally induced thermal states , Ann. Phys. 141, 201 (1982)

    1982

  4. [12]

    Takagi, Vacuum Noise and Stress Induced by Uniform Acceleration , Prog

    S. Takagi, Vacuum Noise and Stress Induced by Uniform Acceleration , Prog. Theor. Phys. Suppl. 88, 1 (1986)

    1986

  5. [13]

    Arrechea, C

    J. Arrechea, C. Barcel´ o, L. J. Garay, and G. Garc ´ ıa-Moreno,Inversion of statistics and thermalization in the Unruh effect , Phys. Rev. D 104, 065004 (2021)

    2021

  6. [14]

    Benatti and R

    F. Benatti and R. Floreanini, Entanglement generation in uniformly accelerating atoms: reexamination of the Unruh effect , Phys. Rev. A 70, 012112 (2004)

    2004

  7. [15]

    Yu and J

    H. Yu and J. Zhang, Understanding Hawking radiation in the framework of open quantum systems, Phys. Rev. D 77, 024031 (2008)

    2008

  8. [16]

    Yu, Open quantum system approach to Gibbons-Hawking effect of de Sitter space-time , Phys

    H. Yu, Open quantum system approach to Gibbons-Hawking effect of de Sitter space-time , Phys. Rev. Lett. 106, 061101 (2011). – 33 –

    2011

  9. [17]

    Kaplanek and C.P

    G. Kaplanek and C.P. Burgess, Hot accelerated qubits: decoherence, thermalization, secular growth and reliable late-time predictions , J. High Energy Phys. 03 (2020) 008

    2020

  10. [18]

    Kaplanek and C.P

    G. Kaplanek and C.P. Burgess, Qubits on the horizon: decoherence and thermalization near black holes , J. High Energy Phys. 01 (2021) 098

    2021

  11. [19]

    J. Feng, Y. -Z. Zhang, M. D. Gould, and H. Fan, Uncertainty relation in Schwarzschild spacetime, Phys. Lett. B 743, 198 (2015)

    2015

  12. [20]

    L. Jia, Z. Tian, and J. Jing, Entropic uncertainty relation in de Sitter space , Ann. Phys. 353, 37 (2015)

    2015

  13. [21]

    Hu and H

    J. Hu and H. Yu, Geometric phase outside a Schwarzschild black hole and the Hawking effect, J. High Energy Phys. 09 (2012) 062

    2012

  14. [22]

    Tian and J

    Z. Tian and J. Jing, Geometric phase of two-level atoms and thermal nature of de Sitter spacetime, J. High Energy Phys. 04 (2013) 109

    2013

  15. [23]

    Feng, J.-J

    J. Feng, J.-J. Zhang, and Y. Zhou, Thermality of the Unruh effect with intermediate statistics, Europhys. Lett. 137, 60001 (2022)

    2022

  16. [24]

    S.-W. Han, Z. Ouyang, Z. Hu, and J. Feng, Relative entropy formulation of thermalization process in a Schwarzschild spacetime , Phys. Lett. B 861 (2025) 139235

    2025

  17. [25]

    Fukuma, S

    M. Fukuma, S. Sugishita, and Y. Sakatani, Master equation for the Unruh-DeWitt detector and the universal relaxation time in de Sitter space , Phys. Rev. D 89, 064024 (2014)

    2014

  18. [26]

    Kaplanek and C.P

    G. Kaplanek and C.P. Burgess, Hot cosmic qubits: late-time de Sitter evolution and critical slowing down , J. High Energ. Phys 02 (2020) 053

    2020

  19. [27]

    Burgess, R

    C.P. Burgess, R. Holman, G. Kaplanek, J. Marting and V. Vennin, Minimal decoherence from inflation, J. Cosmol. Astropart. 07 (2023) 022

    2023

  20. [28]

    Breuer and F

    H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press 2002)

    2002

  21. [29]

    Kaplanek and E

    G. Kaplanek and E. Tjoa, Effective master equations for two accelerated qubits , Phys. Rev. A 107, 012208 (2023)

    2023

  22. [30]

    Moustos and C

    D. Moustos and C. Anastopoulos, Non-Markovian time evolution of an accelerated qubit , Phys. Rev. D 95, 025020 (2017)

    2017

  23. [31]

    Moustos, Asymptotic states of accelerated detectors and universality of the Unruh effect , Phys

    D. Moustos, Asymptotic states of accelerated detectors and universality of the Unruh effect , Phys. Rev. D 98, 065006 (2018)

    2018

  24. [32]

    Mottola, Particle creation in de Sitter space , Phys

    E. Mottola, Particle creation in de Sitter space , Phys. Rev. D 31, 754 (1985)

    1985

  25. [33]

    Allen, Vacuum states in de Sitter space , Phys

    B. Allen, Vacuum states in de Sitter space , Phys. Rev. D 32, 3136 (1985)

    1985

  26. [34]

    M. B. Einhorn and F. Larsen, Interacting quantum field theory in de Sitter vacua , Phys. Rev. D 67, 024001 (2003)

    2003

  27. [35]

    Goldstein and D

    K. Goldstein and D. A. Lowe, A note on α-vacua and interacting field theory in de Sitter space, Nucl. Phys. B 669, 325 (2003)

    2003

  28. [36]

    Collins, R

    H. Collins, R. Holman, and M. R. Martin, The fate of the alpha-vacuum , Phys. Rev. D 68, 124012 (2003)

    2003

  29. [37]

    de Boer, V

    J. de Boer, V. Jejjala, and D. Minic, α-states in de Sitter space , Phys. Rev. D 71, 044013 (2005). – 34 –

    2005

  30. [38]

    U. H. Danielsson, Inflation, holography, and the choice of vacuum in de Sitter space , J. High Energy Phys. 07 (2002) 040

    2002

  31. [39]

    U. H. Danielsson, Note on inflation and trans-Planckian physics , Phys. Rev. D 66, 023511 (2002)

    2002

  32. [40]

    Goldstein and D

    K. Goldstein and D. A. Lowe, Quantum initial conditions for inflation and canonical invariance, Phys. Rev. D 69, 023507 (2004)

    2004

  33. [41]

    Bousso, A

    R. Bousso, A. Maloney and A. Strominger, Conformal vacua and entropy in de Sitter space , Phys. Rev. D 65, 104039 (2002)

    2002

  34. [42]

    Danielsson, The quantum swampland , J

    U. Danielsson, The quantum swampland , J. High Energy Phys. 04, 095 (2019)

    2019

  35. [43]

    Aspachs, G

    M. Aspachs, G. Adesso, and I. Fuentes, Optimal Quantum Estimation of the Unruh-Hawking Effect, Phys. Rev. Lett. 105, 151301 (2010)

    2010

  36. [44]

    Z. Tian, J. Wang, H. Fan, and J. Jing, Relativistic Quantum Metrology in Open System Dynamics, Sci. Rep. 5, 7946 (2015)

    2015

  37. [45]

    Feng and J.-J

    J. Feng and J.-J. Zhang, Quantum Fisher information as a probe for Unruh thermality , Phys. Lett. B 827, 136992 (2022)

    2022

  38. [46]

    J. Wang, Z. Tian, J. Jing, and H. Fan, Parameter estimation for an expanding universe , Nucl. Phys. B 892, 390 (2015)

    2015

  39. [47]

    Du and R

    H. Du and R. B. Mann, Fisher information as a probe of spacetime structure: Relativistic quantum metrology in (A)dS , J. High Energ. Phys 05 (2021) 112

    2021

  40. [48]

    Pattersona and R

    E. Pattersona and R. B. Mann, Fisher information of a black hole spacetime , J. High Energ. Phys. 06 (2023) 214

    2023

  41. [49]

    Huang, J

    X. Huang, J. Feng, Y.Z. Zhang, and H. Fan, Quantum estimation in an expanding spacetime, Ann. Phys. 397, 336 (2018)

    2018

  42. [50]

    Breuer, E.-M

    H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, Colloquium: Non-Markovian dynamics in open quantum systems , Rev. Mod. Phys. 88, 021002 (2016)

    2016

  43. [51]

    E. B. Davies, Markovian Master Equations , Commun. Math. Phys. 39, 91 (1974)

    1974

  44. [52]

    J. Feng, X. Huang, Y.-Z. Zhang, and H. Fan, Bell inequalities violation within non-Bunch-Davies states , Phys. Lett. B 786, 403 (2018)

    2018

  45. [53]

    F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University Press 2010), pp. 612

    2010

  46. [54]

    C. W. Helstrom, Quantum detection and estimation theory , J. Stat. Phys. 1, 231 (1969)

    1969

  47. [55]

    S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states , Phys. Rev. Lett. 72, 3439 (1994)

    1994

  48. [56]

    M. G. A. Paris, Quantum estimation for quantum technology , Int. J. Quantum Inf. 7, 125 (2009)

    2009

  49. [57]

    G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists , 6th Edition (Academic Press 2005)

    2005

  50. [58]

    Spradlin and A

    M. Spradlin and A. Volovich, Vacuum states and the S matrix in dS/CFT , Phys. Rev. D 65, 104037 (2002). – 35 –

    2002

  51. [59]

    Kanno, J

    S. Kanno, J. Murugan, J. P. Shock and J. Soda, Entanglement entropy of α-vacua in de Sitter space, J. High Energ. Phys. 07 (2014) 072

    2014

  52. [60]

    Ryu and T

    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT , Phys. Rev. Lett. 96 (2006) 181602

    2006

  53. [61]

    R. H. Brandenberger and J. Martin, Trans-Planckian issues for inflationary cosmology , Class. Quantum Grav. 30 (2013) 113001

    2013

  54. [62]

    R. H. Brandenberger, Initial conditions for inflation — A short review , Int. J. Mod. Phys. D 26, 1740002 (2017)

    2017

  55. [63]

    Kaloper, M

    N. Kaloper, M. Kleban, A. Lawrence, S. Shenker and L. Susskind, Initial conditions for inflation, J. High Energy Phys. 11, 037 (2002)

    2002

  56. [64]

    Danielsson, On the consistency of de Sitter vacua , J

    U. Danielsson, On the consistency of de Sitter vacua , J. High Energy Phys. 12, 025 (2012)

    2012

  57. [65]

    Shukla, S

    A. Shukla, S. P. Trivedi and V. Vishal, Symmetry constraints in inflation, α-vacua, and the three point function, J. High Energy Phys. 12, 102 (2016)

    2016

  58. [66]

    P. A. R. Ade, et al. , Planck Collaboration, Planck 2015 results XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20

    2016

  59. [67]

    H. P. Breuer, E. Laine, J. Piilo, and B. Vacchini, Non-Markovian dynamics in open quantum systems , Rev. Mod. Phys. 88, 021002 (2016)

    2016

  60. [68]

    Brahma, A

    S. Brahma, A. Berera and J. Calder´ on-Figueroa, Quantum corrections to the primordial tensor spectrum: open EFTs & Markovian decoupling of UV modes , J. High Energy Phys. 08, 225 (2022)

    2022

  61. [69]

    P. O. Fedichev and U. R. Fischer, Gibbons-Hawking Effect in the Sonic de Sitter Space-Time of an Expanding Bose-Einstein-Condensed Gas , Phys. Rev. Lett. 91, 240407 (2003)

    2003

  62. [70]

    J. S. Sidhu and P. Kok, Geometric perspective on quantum parameter estimation , A VS Quantum Sci. 2, 014701 (2020)

    2020

  63. [71]

    Lambert and E

    J. Lambert and E. S. Sørensen, From classical to quantum information geometry: a guide for physicists , New J. Phys. 25, 081201 (2023). – 36 –

    2023

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.