Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector

Dong Wang; Li-Juan Li; Liu Ye; Xue-Ke Song

REVIEW 4 major objections 3 minor 1 cited by

Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector

T0 review · 4 major / 3 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read An Unruh-DeWitt detector in de Sitter and Anti-de Sitter spacetimes reaches the same late-time measurement uncertainty and quantum coherence, both determined only by the ratio Ω/T of its energy gap to the temperature.

desk verdict The paper's headline claim of nonzero late-time coherence in dS and AdS is contradicted by its own Bloch solution, so the main result fails; only the transient dynamics are worth a second look. read the letter →

arxiv 2502.07167 v1 pith:DYUC7FJG submitted 2025-02-11 hep-th quant-ph

Li-Juan Li , Xue-Ke Song , Liu Ye , Dong Wang This is my paper · ORCID

classification hep-thquant-ph

keywords Unruh-DeWittdetectordeSitterspacetimeAnti-deentropicuncertaintyrelationquantumcoherenceopensystemsGibbons-Hawkingeffectconformalvacuum

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 argues that a two-level Unruh-DeWitt detector coupled to a massless scalar field in the conformal vacuum of de Sitter spacetime and of Anti-de Sitter spacetime thermalizes to the same late-time state. As a result, the entropic measurement uncertainty and the $\ell^1$-norm quantum coherence of the detector settle at constant values that are identical in the two backgrounds and depend only on the ratio Ω/T of the detector's energy gap to the environment temperature. Larger Ω/T yields lower uncertainty and higher coherence, while acceleration in dS and boundary conditions in AdS affect only the transient early-time dynamics, not the asymptotic values. If correct, this gives a spacetime-independent late-time benchmark for quantumness probed by such detectors and a simple design rule: raise the energy gap relative to temperature to protect coherence and reduce uncertainty.

What carries the argument

The carrying mechanism is the weak-coupling Markovian open-system dynamics: the field is traced out to give the Kossakowski-Lindblad master equation (23), whose coefficients are built from the detector's response functions $G(\pm\Omega)$ in each spacetime. The Bloch-vector solution (28)-(29) exhibits exponential decay of the coherences and relaxation of the populations, so the initial superposition oscillations die out and the detector converges to the Gibbs-like fixed point (33). The response functions encode the spacetime (Gibbons-Hawking and Unruh temperatures, AdS boundary condition), but the fixed point itself depends only on $\Omega/T$.

What would settle it

Simulate the full detector-field dynamics beyond the Markovian approximation in dS and AdS at finite coupling; if the long-time density matrix differs from the Gibbs form of Eq. (33) — for instance, if the off-diagonal element is not $\frac{i}{2}\tanh(\Omega/2T)$ or the populations are not $1/(1+e^{\mp\Omega/T})$ — then the claimed $\Omega/T$ universality is an artifact of the weak-coupling master equation.

Watch

Extended reading notes

Core claim

The paper claims that once the Unruh-DeWitt detector has interacted with the conformal vacuum for a long time, its state becomes the thermal state given in Eq. (33), with occupation probabilities $1/(1+e^{\mp\Omega/T})$ and off-diagonal coherence $\pm \frac{i}{2}\tanh(\Omega/2T)$. From this state, the entropic uncertainty $U_s$ and $\ell^1$-norm coherence $C_s$ take the same constant values in dS and AdS, as stated in Eqs. (34)-(35) and (39)-(40), so acceleration in dS and the Dirichlet, transparent, and Neumann boundary conditions in AdS are washed out by thermalization. The only parameter that controls the quantumness at late times is the ratio $\Omega/T$: larger $\Omega/T$ monotonically lowers $U_s$ and raises $C_s$.

Load-bearing premise

The result assumes the detector couples weakly to the field and that the field acts as a memoryless environment, so the detector relaxes to the thermal Gibbs state; if non-Markovian memory or back-reaction matters, the claimed $\Omega/T$-only final state need not hold.

Editorial extensions

If this is right

A detector with the same energy gap and temperature will report identical final uncertainty and coherence whether it sits in dS or AdS, so the late-time quantumness is a curvature-independent calibration.
Increasing the detector's energy gap relative to the ambient temperature monotonically reduces final measurement uncertainty and increases final l1 coherence.
Acceleration in dS and boundary conditions in AdS affect only the transient approach; an initially superposed detector oscillates in uncertainty and coherence at low temperature, and higher temperature suppresses those oscillations.
Because the fixed point has off-diagonal coherence $\frac{i}{2}\tanh(\Omega/2T)$, the detector's late-time coherence is a direct readout of $\Omega/T$, and in AdS the detector thermalizes faster than in dS at the same temperature.

Reading between the lines

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

An implicit design consequence the paper does not spell out is that a curved-spacetime qubit could preserve quantum coherence by choosing a large energy gap relative to the local temperature, since the universal late-time coherence grows with $\Omega/T$.
The same $\Omega/T$ universality may plausibly hold for other detector-field models or vacua that share the same Markovian thermal fixed point, but extending the argument beyond dS and AdS would require a separate proof.
A non-Markovian or strong-coupling extension would be the natural test of whether the universal late-time state survives outside the weak-coupling, memoryless approximation that the paper explicitly invokes.

Share X Bluesky LinkedIn Reddit HN

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

You should know two things before spending time on this paper. First, the central late-time coherence claim is internally inconsistent. The Bloch solution in Eqs. (28)-(29) gives n1 and n2 decaying to zero, so ρ(∞) is diagonal and the l1-norm coherence defined in Eq. (7) is exactly zero. But Eqs. (33) and (35) present off-diagonal elements ±(i/2)tanh(Ω/2T) and a positive C_s. These cannot both follow from the same master equation. Worse, the matrix in Eq. (33) fails positivity for Ω/T ≳ 1.76, so the displayed final state is not a density matrix in that regime. This is not a minor typo; it kills the headline result.

Second, what is actually new is the transient behavior. The paper cleanly sets up the UDW detector plus Lindblad master equation and produces explicit formulas for early-time uncertainty and coherence in dS and AdS, including the effects of acceleration and of Dirichlet/transparent/Neumann boundary conditions. The qualitative features—oscillations for superposition initial states, suppression at high temperature, the fading influence of acceleration and boundary conditions as T grows—are consistent with the figures and are plausible. If one restricts attention to the uncertainty branch, Us depending only on Ω/T is a reasonable thermalization statement.

The soft spots are serious. The coherence branch is not a side issue; it carries the claimed spacetime-independent 'quantumness.' The dS/AdS equality at late times is a trivial consequence of the detailed-balance Lindblad form with a common temperature, not an independent output. There are also smaller signs of carelessness: the free Hamiltonian in Eq. (2) has the ground and excited energies reversed relative to the usual convention, and the initial-state parameter θ is easy to misread. The non-Markovian back-reaction worry is real but secondary; the internal contradiction is sufficient on its own.

Who should read this? Researchers in relativistic quantum information might find the transient formulas useful as a reference, but the paper in its current form cannot be trusted as a source for the late-time coherence value.

My recommendation: desk reject rather than send to referees. The main claim is demonstrably false from the paper's own equations. If the authors revise—dropping the nonzero late-time coherence claim and presenting the transient results on their own—the early-time material could be worth a resubmission. I would not cite it as is, and I would not bring it to a reading group.

Referee Report

4 major / 3 minor

Summary. The manuscript investigates an Unruh-DeWitt detector coupled to a massless scalar field in de Sitter and Anti-de Sitter spacetimes, treating the detector as an open quantum system. It solves a Lindblad master equation via a Bloch-vector ansatz and computes the entropic uncertainty and l1-norm coherence of the detector state during its evolution. The central claim is that at late times both uncertainty and coherence approach constants that are identical for dS and AdS spacetimes and depend only on the ratio Ω/T of the detector energy gap to the temperature.

Significance. If established, the claimed Ω/T-universality of late-time detector quantumness would provide a clean, spacetime-independent benchmark for probing quantum information in curved backgrounds. The paper assembles a reasonable open-systems framework and gives explicit response functions for the relevant detector trajectories, which are useful ingredients. However, the late-time coherence result is internally inconsistent with the paper's own master-equation solution, and the advertised universality for coherence is not supported. The uncertainty part may survive in some form, but the central claim as presented fails.

major comments (4)

[Section IV, Eqs. (29) and (33)] The Bloch solution in Eq. (29) gives n1(τ) and n2(τ) both proportional to e^{-A'τ/2}, so they vanish as τ→∞. The resulting ρ(∞) is therefore diagonal, and the l1-norm coherence defined in Eq. (7) is identically zero. Equation (33), however, displays off-diagonal elements ±(i/2)tanh(Ω/2T), and Eq. (35) derives C_s = tanh(Ω/2T). These two expressions for the same late-time state cannot both follow from the same master equation; a nonzero late-time coherence is not supported by the calculation.
[Section IV, Eq. (33)] Even if Eq. (33) were intended as a formal ansatz for the asymptotic state, it is not positive semidefinite for all parameter values: its determinant is (3 - cosh(Ω/T)) / (4(1 + cosh(Ω/T))), which becomes negative for Ω/T ≳ 1.76. A matrix with negative determinant cannot be a valid density matrix at any time, so Eq. (33) cannot represent the late-time state of a legitimate Lindblad evolution.
[Section V, Eqs. (39)-(40)] The claim that the late-time constant values of uncertainty and coherence are identical in dS and AdS and depend only on Ω/T is unsupported, because it relies directly on Eqs. (33) and (35). If the late-time state is instead the diagonal thermal state implied by Eq. (29), the coherence is exactly zero in both spacetimes, and the advertised 'identical coherence' result disappears.
[Section IV, Eqs. (30)-(32)] The transient coherence formula in Eq. (32) is inconsistent with the density matrix in Eqs. (28)-(29). From Eq. (29), the off-diagonal element of ρ(τ) has modulus (1/2)e^{-A'τ/2} sinθ, which decays monotonically and does not oscillate. Equation (32), via m1 = e^{μ1} sinθ cos(Ω̃τ), predicts oscillatory coherence. The oscillations displayed in Figs. 1-3 are therefore not consequences of the stated Bloch solution, and the derivation of Eq. (32) appears to be incorrect.

minor comments (3)

[General] There are several typos and unfinished phrases, e.g., 'comving detector' in Section IV, 'the Unruh-DeWitt can be seen' in Section I, and a missing closing parenthesis in the definition of μ1 in Eq. (31).
[Section IV, Fig. 2 and Eq. (20)] The paper treats T and a as independent parameters in the numerical plots, but the physical temperature of an accelerated detector in dS spacetime is T = sqrt(a^2 + 1/l^2)/(2π), which is already used in the response function (20). Sweeping T and a independently therefore explores parameter combinations that do not correspond to a single physical trajectory, and the statements about the role of acceleration should be reconsidered.
[Reference list] Reference [68] contains a typographical error in the author name ('T. Y , Wang'), and Ref. [42] misspells Nielsen as Nielson.

Circularity Check

1 steps flagged · score 6.0 of 10

Late-time coherence 'prediction' is read off from the off-diagonal entries inserted into Eq. (33), not derived from the Bloch solution (29).

self definitional [Section IV, Eqs. (33)-(35)]
"When τ → ∞, the final state of the system can be expressed as ρ(∞) = ( 1/(1+e^{-Ω/T}) −(1/2)i tanh(Ω/2T); (1/2)i tanh(Ω/2T) 1/(1+e^{Ω/T}) ). ... C_s^{dS}(τ→∞)= |−1/2 i tanh(Ω/2T)| + |1/2 i tanh(Ω/2T)|."

The master-equation solution in Eq. (29) gives n1(τ)=e^{-A'τ/2} sinθ cos(Ω̃τ) and n2(τ)=e^{-A'τ/2} sinθ sin(Ω̃τ), so as τ→∞ both vanish. Therefore the state ρ(∞) from Eq. (28) is diagonal, and the l1-norm coherence defined in Eq. (7) is exactly zero. The off-diagonal entries ±(1/2)i tanh(Ω/2T) in Eq. (33) are not produced by the dynamics; they are inserted into the asserted final state. Eq. (35) then simply sums the moduli of those inserted entries. Hence the claimed late-time coherence C_s=tanh(Ω/2T) is equivalent, by construction, to the off-diagonal elements written into Eq. (33), rather than being a prediction derived from the Lindblad evolution.

full rationale

The late-time uncertainty result Us is not circular: it follows from the Bloch solution Eq. (29), with n3∞=-R and R=B'/A'. Using the detailed-balance property G(-Ω)=e^{Ω/T}G(Ω) shared by the response functions (19)-(21), one obtains R=-tanh(Ω/2T), so Us depends only on Ω/T. That is a legitimate corollary of the assumed Lindblad thermalization, not a fitted parameter. By contrast, the late-time coherence claim C_s=tanh(Ω/2T) is built into the asserted final state: Eq. (29) forces the off-diagonal elements to vanish, yet Eq. (33) inserts ±(i/2)tanh(Ω/2T), and Eq. (35) returns their moduli as the 'predicted' coherence. This is a reduction-by-construction. The self-citations in the introduction (e.g., Refs. [50]-[54]) are not load-bearing for the central derivation, and the response functions and master equation are cited to independent prior work. Overall, the Ω/T-universal uncertainty is a genuine consequence of detailed balance, but the Ω/T-universal coherence is an input relabeled as an output, giving partial circularity.

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

No new particles, forces, fields, or spacetime structures are introduced. The quantities scanned in the figures (Omega, T, a, l, zeta, theta) are physical model inputs, not constants fitted to data; the central Omega/T dependence is a property of the thermal response functions, not a fitted relation. The main burden is carried by the Markovian master-equation assumption and by the cited response functions.

assumptions (5)

domain assumption Weak coupling and Markovian approximation justify the Kossakowski-Lindblad master equation (23) for the detector.
Stated in Sec. III above Eq. (23). The late-time thermal state and the Omega/T dependence follow from this master-equation form.
domain assumption The response functions in Eqs. (19)-(21), taken from Refs. [9, 71, 74-76], correctly encode the field vacuum and the detector trajectory in dS and AdS.
These functions set A', B', and hence the decay rates and final state.
domain assumption The field is prepared in the conformal vacuum (dS) and the corresponding vacuum (AdS), and the detector starts in a product state with that vacuum.
Sec. II.B and Sec. III; changing the vacuum changes the Wightman function and the response.
standard math The Maassen-Uffink entropic uncertainty relation and the l1-norm coherence definition apply to the reduced detector state.
Eqs. (5) and (7); established formalisms used as diagnostics.
standard math The Hilbert transform K(omega) defining the renormalized gap Omega-tilde is well-defined and the principal-value integral converges.
Eq. (27); the paper does not evaluate it, and the oscillation frequency depends on Omega-tilde.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector." pith.science (2026). https://pith.science/paper/DYUC7FJG

@misc{pith2026250207167,
  author       = {Pith},
  title        = {Pith review of: Quantifying Quantumness in (A)dS spacetimes with Unruh-DeWitt Detector},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DYUC7FJG}},
  note         = {Machine review of arXiv:2502.07167}
}

read the original abstract

Probing quantumness in curved spacetime is regarded as one of fundamental and important topics in the framework of relativistic quantum information. In this work, we focus on the theoretical feasibility of probing quantum properties in de Sitter (dS) and Anti-de Sitter (AdS) spacetimes via detectors. By employing the Unruh-DeWitt detector coupled with a massless scalar field, which is treated as an open system, quantum uncertainty and quantum coherence in both dS and AdS spacetimes are investigated. Our analysis reveals that the acceleration in dS spacetime and the boundary conditions in AdS spacetime significantly impact the detector's evolution in the initial stage. Notably, both of the uncertainty and coherence will oscillate with the initial state being in a superposition state, however the high temperature is able to suppress their oscillation. Interestingly, it is found that the constant values of the final uncertainty and coherence are identical as those in dS and AdS spacetimes, which are determined by the ratio of energy gap to temperature. Hence, the current exploration offers insight into quantumness in dS and AdS spacetimes, and might be helpful to facilitate the curved-spacetime-based quantum information processing.

Figures

Figures reproduced from arXiv: 2502.07167 by the authors.

**Figure 1.** FIG. 1. The time evolution of measurement uncertainty and coherence probed by comoving detector in dS spacetime. (a) The time evolution of [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** FIG. 2. The effect of acceleration on the measurement uncertainty [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3. The effect of acceleration on the quantum coherence [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4. (a) The constant value of measurement uncertainty [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. The effect of boundary condition on the measurement uncertainty [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: FIG. 6. The effect of boundary condition on the quantum coherence [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

Relativistic Quantum Thermometry in AdS Spacetime via Non-Markovian Temperature Sensing
quant-ph 2026-07 conditional novelty 5.0 of 10

An ancillary Unruh-DeWitt detector mediates thermal information from an AdS spacetime to a protected probe qubit, enhancing non-Markovian quantum thermometric precision.

Reference graph

Works this paper leans on

77 extracted references · 59 canonical work pages · cited by 1 Pith paper

[1]

R. B. Mann and T. C. Ralph, Class. Quant. Grav. 29, 220301 (2012)

work page 2012
[2]

(13) The massless scalar field ϕ conformally coupled to curvature via the action S = Z √−g[ 1 2 gµν∇µϕ∇νϕ − 1 12 Rϕ2]

(11) In addition to the static metric, we also consider the comoving coordinates for dS4, the corresponding transformations    T = l sinh(t/l) + r2et/l 2l , X0 = l cosh(t/l) − r2et/l 2l , X1 = et/lx1, X2 = et/lx2, X3 = et/lx3, (12) then we end up with the comoving metric ds2 = −dt2 + e2t/l(dx2 1 + dx2 2 + dx2 3). (13) The massless scalar fiel...

work page 2001
[3]

W. G. Unruh, Phys. Rev. D 14, 870 (1976)

1976
[4]

B. S. DeWitt, Quantum gravity: the new synthesis, in General relativity: An Einstein Centenary Survey, ed. by S. Hawking and W. Israels, (Cambridge University Press 1979)

work page 1979
[5]

X. Y . Huang, J. Feng, Y . Z. Zhang, and H. Fan, Ann. Phys.397, 336 (2018)

work page 2018
[6]

Benatti and R

F. Benatti and R. Floreanini, Phys. Rev. A 70, 012112 (2004)

work page 2004
[7]

Du and R

H. Du and R. B. Mann, JHEP 05, 112 (2021)

work page 2021
[8]

Patterson and R

E. Patterson and R. B. Mann, JHEP 06, 214 (2023)

work page 2023

Show all 77 references

[9]

Louko and A

J. Louko and A. Satz, Class. Quant. Grav. 25, 055012 (2008)

2008
[10]

Jennings, Class

D. Jennings, Class. Quant. Grav. 27, 205005 (2010)

2010
[11]

G. L. Sewell, Ann. Phys. 141, 201 (1982)

1982
[12]

S. W. Hawking, Commun. Math. Phys. 43, 199 (1975)

1975
[13]

Heisenberg, Z

W. Heisenberg, Z. Phys. 43, 172 (1927)

1927
[14]

Baumgratz, M

T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)

2014
[15]

P. J. Coles and M. Piani, Phys. Rev. A 89, 022112 (2014)

2014
[16]

M. L. Hu and H. Fan, Phys. Rev. A 86, 032338 (2012)

2012
[17]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, Phys. Rev. Lett. 88, 127902 (2002)

2002
[18]

Grosshans and N

F. Grosshans and N. J. Cerf, Phys. Rev. Lett.92, 047905 (2004)

2004
[19]

Koashi, J

M. Koashi, J. Phys. Conf. Ser. 36, 98 (2006)

2006
[20]

Schneeloch, C

J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell, Phys. Rev. A 87, 062103 (2013)

2013
[21]

S. P. Walborn, A. Salles, R. M. Gomes, F. Toscano, and P. H. Souto Ribeiro, Phys. Rev. Lett. 106, 130402 (2011)

2011
[22]

P. J. Coles, J. Kaniewski, and S. Wehner, Nat. Commun.5, 5814 (2014)

2014
[23]

G. M. Bosyk, M. Portesi, F. Holik, and A. Plastino, Phys. Scr. 87, 065002 (2013)

2013
[24]

Jarzyna and R

M. Jarzyna and R. Demkowicz-Dobrza ´nski, New J. Phys. 17, 013010 (2015)

2015
[25]

Vallone, D

G. Vallone, D. G. Marangon, M. Tomasin, and P. Villoresi, Phys. Rev. A 90, 052327 (2014)

2014
[26]

C. H. Bennett, G. Brassard, C. Cr ´epeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett.70, 1895 (1993)

1993
[27]

K ¨onig, S

R. K ¨onig, S. Wehner, and J. W ¨ullschleger, IEEE Trans. Inf. Theory 58, 1962 (2012)

2012
[28]

Dupuis, O

F. Dupuis, O. Fawzi, and S. Wehner, IEEE Trans. Inf. Theory 61, 1093 (2015)

2015
[29]

Y . Y . Yang, L. Ye, and D. Wang, Ann. Phys. (Berlin) 532, 2000062 (2020)

2020
[30]

Ahmadi, D

M. Ahmadi, D. E. Bruschi, C. Sab´ın, G. Adesso, and I. Fuentes, Sci. Rep. 4, 4996 (2014)

2014
[31]

Aspachs, G

M. Aspachs, G. Adesso, and I. Fuentes, Phys. Rev. Lett. 105, 151301 (2010)

2010
[32]

J. Wang, Z. Tian, J. Jing, and H. Fan, Nucl. Phys. B 892, 390 (2015)

2015
[33]

Sab ´ın, D

C. Sab ´ın, D. E. Bruschi, M. Ahmadi, and I. Fuentes, New J. Phys. 16, 085003 (2014)

2014
[34]

Sch ¨utzhold, Phys

R. Sch ¨utzhold, Phys. Rev. D 98, 105019 (2018)

2018
[35]

M. P. G. Robbins, N. Afshordi, and R. B. Mann, JCAP 07, 032 (2019)

2019
[36]

D. E. Bruschi, A. Datta, R. Ursin, T. C. Ralph, and I. Fuentes, Phys. Rev. D 90, 124001 (2014)

2014
[37]

E. H. Kennard, Z. Phys. 44, 326 (1927)

1927
[38]

H. P. Robertson, Phys. Rev. 34, 163 (1929)

1929
[39]

Deutsch, Phys

D. Deutsch, Phys. Rev. Lett. 50, 631 (1983)

1983
[40]

Kraus, Phys

K. Kraus, Phys. Rev. D 35, 3070 (1987)

1987
[41]

Maassen and J

H. Maassen and J. Uffink, Phys. Rev. Lett. 60, 1103 (1988)

1988
[42]

Berta, M

M. Berta, M. Christandl, R. Colbeck, J. M. Renes, and R. Ren- ner, Nat. Phys. 6, 659 (2010)

2010
[43]

M. A. Nielson and I. L. Chuang, Quantum Computation and Quantum Information, (Cambridge University Press, Cam- bridge, 2002)

2002
[44]

Z. Y . Xu, S. Q. Zhu, and W. L. Yang, Appl. Phys. Lett. 101, 244105 (2012)

2012
[45]

D. Wang, F. Ming, A. J. Huang, W. Y . Sun, J. D. Shi, and L. Ye, Laser Phys. Lett. 14, 055205 (2017)

2017
[46]

D. Wang, F. Ming, X. K. Song, L. Ye, and J. L. Chen, Eur. Phys. J. C 80, 800 (2020)

2020
[47]

L. J. Li, F. Ming, X. K. Song, L. Ye, and D. Wang, Eur. Phys. J. C 81, 728 (2021)

2021
[48]

Blasone, S

M. Blasone, S. De Siena, and C. Matrella, Eur. Phys. J. C 81, 660 (2021)

2021
[49]

Korzekwa, M

K. Korzekwa, M. Lostaglio, D. Jennings, and T. Rudolph, Phys. Rev. A 89, 042122 (2014)

2014
[50]

L. J. Li, F. Ming, W. N. Shi, L. Ye, and D. Wang, Physica E 133, 114802 (2021)

2021
[51]

J. Feng, Y . Z. Zhang, M. D. Gould, and H. Fan, Phys. Lett. B 743, 198 (2015)

2015
[52]

D. Wang, W. N. Shi, R. D. Hoehn, F. Ming, W. Y . Sun, S. Kais, and L. Ye, Ann. Phys. (Berlin) 530, 1800080 (2018)

2018
[53]

J. L. Huang, F. W. Shu, Y . L. Xiao, and M. H. Yung, Eur. Phys. J. C 78, 545 (2018)

2018
[54]

L. J. Li, F. Ming, X. K. Song, L. Ye, and D. Wang, Eur. Phys. J. C 82, 726 (2022)

2022
[55]

T. Y . Wang and D. Wang, Phys. Lett. B855, 138876 (2024)

2024
[56]

P. J. Coles, M. Berta, M. Tomamichel, and S. Wehner, Rev. Mod. Phys. 89, 015002 (2017)

2017
[57]

Wehner and A

S. Wehner and A. Winter, New J. Phys. 12, 025009 (2010)

2010
[58]

Pramanik, P

T. Pramanik, P. Chowdhury, and A. S. Majumdar, Phys. Rev. Lett. 110, 020402 (2013)

2013
[59]

Maccone and A

L. Maccone and A. K. Pati, Phys. Rev. Lett. 113, 260401 (2014)

2014
[60]

A. K. Pati, M. M. Wilde, A. R. Usha Devi, A. K. Rajagopal, and Sudha, Phys. Rev. A 86, 042105 (2012)

2012
[61]

Ollivier and W

H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)

2001
[62]

M. L. Hu and H. Fan, Phys. Rev. A 88, 014105 (2013)

2013
[63]

Adabi, S

F. Adabi, S. Salimi, and S. Haseli, Phys. Rev. A 93, 062123 (2016)

2016
[64]

Haseli and F

S. Haseli and F. Ahmadi, Eur. Phys. J. D 73, 65 (2019)

2019
[65]

B. F. Xie, F. Ming, D. Wang, L. Ye, and J. L. Chen, Phys. Rev. A 104, 062204 (2021)

2021
[66]

F. Ming, D. Wang, X. G. Fan, W. N. Shi, L. Ye, and J. L. Chen, Phys. Rev. A 102, 012206 (2020)

2020
[67]

Dolatkhah, S

H. Dolatkhah, S. Haseli, S. Salimi, and A. S. Khorashad, Phys. Rev. A 102, 052227 (2020)

2020
[68]

L. Wu, L. Ye, and D. Wang, Phys. Rev. A 106, 062219 (2022)

2022
[69]

Y , Wang and D

T. Y , Wang and D. Wang, Phys. Lett. A499, 129364 (2024)

2024
[70]

Streltsov, G

A. Streltsov, G. Adesso, and M. B. Plenio, Rev. Mod. Phys. 89, 041003 (2017)

2017
[71]

M. L. Hu, X. Hu, J. C. Wang, Y . Peng, Y . R. Zhang, and H. Fan, Phys. Rep. 762, 1 (2018)

2018
[72]

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

1982
[73]

S. J. Avis, C. J. Isham, and D. Storey, Phys. Rev. D 18, 3565 (1978). 12

1978
[74]

G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2738 (1977)

1977
[75]

Deser and O

S. Deser and O. Levin, Class. Quant. Grav. 14, L163 (1997)

1997
[76]

Narnhofer, I

H. Narnhofer, I. Peter, and W. E. Thirring, Int. J. Mod. Phys. B 10, 1507 (1996)

1996
[77]

Casadio, S

R. Casadio, S. Chiodini, A. Orlandi, G. Acquaviva, R. Di Cri- scienzo, and L. Vanzo, Mod. Phys. Lett. A 26, 2149 (2011)

2011

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

R. B. Mann and T. C. Ralph, Class. Quant. Grav. 29, 220301 (2012)

work page 2012

[2] [2]

(13) The massless scalar field ϕ conformally coupled to curvature via the action S = Z √−g[ 1 2 gµν∇µϕ∇νϕ − 1 12 Rϕ2]

(11) In addition to the static metric, we also consider the comoving coordinates for dS4, the corresponding transformations    T = l sinh(t/l) + r2et/l 2l , X0 = l cosh(t/l) − r2et/l 2l , X1 = et/lx1, X2 = et/lx2, X3 = et/lx3, (12) then we end up with the comoving metric ds2 = −dt2 + e2t/l(dx2 1 + dx2 2 + dx2 3). (13) The massless scalar fiel...

work page 2001

[3] [3]

W. G. Unruh, Phys. Rev. D 14, 870 (1976)

1976

[4] [4]

B. S. DeWitt, Quantum gravity: the new synthesis, in General relativity: An Einstein Centenary Survey, ed. by S. Hawking and W. Israels, (Cambridge University Press 1979)

work page 1979

[5] [5]

X. Y . Huang, J. Feng, Y . Z. Zhang, and H. Fan, Ann. Phys.397, 336 (2018)

work page 2018

[6] [6]

Benatti and R

F. Benatti and R. Floreanini, Phys. Rev. A 70, 012112 (2004)

work page 2004

[7] [7]

Du and R

H. Du and R. B. Mann, JHEP 05, 112 (2021)

work page 2021

[8] [8]

Patterson and R

E. Patterson and R. B. Mann, JHEP 06, 214 (2023)

work page 2023