Entangled Quantum Negative Energy Teleportation as a Probe of Semiclassical Gravity

Daniel S. Zachary

REVIEW 4 major objections 3 minor 31 references

Entangled Quantum Negative Energy Teleportation as a Probe of Semiclassical Gravity

T0 review · 4 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that quantum energy teleportation can create localized negative energy whose semiclassical gravitational effects are detectable with atomic clocks, and proposes a traveling curvature pulse as a warp-drive alternative.

desk verdict Good question, broken arithmetic: the paper's detectability claims collapse on the missing c^4 in the curvature conversion and a dimensionally invalid clock formula. read the letter →

arxiv 2506.19878 v1 pith:CCDVSBEQ submitted 2025-06-23 quant-ph

Daniel S. Zachary This is my paper · ORCID

classification quant-ph

keywords quantumenergyteleportationnegativedensitysemiclassicalgravityspacetimecurvatureatomicclocksmetrologyCasimireffectcompression

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

The paper sets out to show that quantum energy teleportation (QET) can create localized negative energy densities large enough to leave a measurable imprint on spacetime through semiclassical gravity. It models each teleportation event as a Gaussian negative-energy pulse, converts that pulse into a curvature dip via the linearized Einstein equation, and then asks whether realistic detectors can see the dip. Its central quantitative claim is that arrays of about 10–100 entangled QET units, aided by squeezing and synchronization, can push the curvature signal above a representative noise floor and produce atomic-clock frequency shifts of $10^{-21}$ to $10^{-17}$, above current clock stability near $10^{-18}$. If correct, this would be the first controlled laboratory probe of gravitational effects sourced by engineered quantum stress-energy. The paper also sketches a speculative extension in which timed QET arrays create a sub-luminal traveling curvature packet as a causal alternative to warp-drive geometries.

What carries the argument

The load-bearing identity is the linearized semiclassical Einstein equation $\delta R(x) = -8\pi G \langle T_{00}(x)\rangle$, which turns an assumed Gaussian negative-energy pulse into a spatial curvature dip. The second piece of machinery is the parametric SNR formula $\mathrm{SNR} \sim (N/d^3)(F/\pi)G_{\mathrm{ent}}G_{\mathrm{shape}}G_{\mathrm{multi}} (1/\sqrt{f})e^{-r}G_{\mathrm{noise}}$, which translates array geometry, cavity finesse, squeezing, and repetition rate into a detection verdict against the noise floor $\sigma_R$.

What would settle it

Compute the renormalized $\langle T_{00}\rangle$ for the QET protocol with the parameters of Table 3, or measure the curvature noise floor of a clock or interferometer array; if the computed peak energy density falls below about $10^{-11}$ J/m$^3$, or the measured $\sigma_R$ exceeds about $10^{-35}$ m$^{-2}$, then no $N\sim10$–$100$ array reaches SNR $>1$ and the central detection claim fails.

Watch

Extended reading notes

Core claim

On the paper's own terms, the core discovery is that the stress-energy left behind by a QET sequence—negative energy density concentrated between the two parties—acts through the semiclassical Einstein equation as a transient source of Ricci curvature. The paper claims each entangled pair contributes a curvature dip of order $\delta R_0 \sim 10^{-36}$ m$^{-2}$, that coherent arrays of $N \sim 10$\u2013$100$ synchronized pairs accumulate this into $\delta R \sim N \delta R_0$, and that with a curvature noise floor $\sigma_R \sim 10^{-35}$ m$^{-2}$ this crosses the SNR $=1$ detection threshold. It further argues that the cleanest observable is atomic clock drift, with fractional shifts $\Delta\tau/\tau$ from $10^{-21}$ to $10^{-17}$ against a $10^{-18}$ stability floor, and that timed arrays can produce a moving, sub-luminal curvature dip (the Quantum-Curvature Compression Channel) without requiring the exotic static stress-energy of warp bubbles.

Load-bearing premise

The paper assumes, without deriving it from the QET Hamiltonian, that each quantum energy teleportation pulse produces a smooth, bell-shaped lump of negative energy about $10^{-11}$ J/m$^3$ with a spread of about a decimetre, and that the detector noise floor for curvature is about $10^{-35}$ m$^{-2}$; if either assumption is wrong, the predicted signals and the required array sizes change accordingly.

Editorial extensions

If this is right

Atomic clock readouts would see fractional time shifts of $10^{-21}$ to $10^{-17}$, above the $10^{-18}$ stability of current optical clocks, using $N \sim 10$\u2013$100$ synchronized QET pairs.
A synchronized QET array would produce a measurable curvature dip $\delta R \sim 10^{-35}$ m$^{-2}$ or larger, which would be the first controlled laboratory signal sourced by quantum stress-energy.
Interferometric phase shifts $\Delta \phi \sim 2\pi \delta R L^2/\lambda$ and strain $h \sim \delta R L^2$ provide independent cross-checks, with strain detection remaining a next-generation prospect.
The parametric model identifies concrete engineering targets: detector spacing near the smearing scale, finesse $10^2$\u2013$10^5$, squeezing $r \sim 1.5$, and repetition near $10^5$ Hz.
Timed QET gates can form a sub-luminal traveling curvature packet (QIX-C), offering a causal laboratory analogue of warp-bubble geometry rather than a superluminal drive.

Reading between the lines

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

A decisive test of the paper's forecast would be a first-principles calculation of $\langle T_{00}\rangle$ from the Unruh–DeWitt Hamiltonian (Eq. 2) to see whether the Gaussian ansatz of Eq. (3) holds at the assumed $\epsilon \sim 10^{-11}$ J/m$^3$ scale.
If atomic clock arrays see this signal, it would be the first observed gravitational response to engineered negative energy, giving a tabletop window into energy-condition violations and the validity of semiclassical gravity.
The QIX-C propagation mechanism, if confirmed in simulations with 3+1 dimensional retarded Green's functions, could be used to study whether synchronized entanglement operations can achieve geodesic compression without superluminality.
Including stochastic stress-tensor fluctuations, which the paper lists as future work, would let the noise floor $\sigma_R$ be predicted rather than assumed, potentially moving the required array size up or down.

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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

Colleague,

This one is a clear reject, but not because the question is bad. The idea of using QET-generated negative energy to probe semiclassical gravity is worth thinking about, and the paper lays out a plausible experimental architecture (entangled units, metrology readout, timing control) in a way that is easy to follow. The SNR parameter scan and the sensitivity contour plots give the reader a sense of what would be needed if the physics worked.

The soft spots are decisive. The linearized relation between Ricci scalar and energy density is written as δR = 8πG (Eq. B.2, A.3). It should be (8πG/c^4). With ε ~ 1e-11 J/m^3, that gives δR ~ 2e-54 m^-2, about 18 orders below the claimed 1e-36. The entire detectability analysis inherits that arithmetic error. The clock-drift formula (Eq. 17) is also dimensionally inconsistent: Δτ/τ ≈ (1/12) δR L^2 Δt has units of seconds, not dimensionless. Restoring the missing c factors would wipe out the claimed 1e-21 to 1e-17 signal against a 1e-18 threshold.

Two other issues compound the arithmetic. The Gaussian negative-energy profile (Eq. 3) is assumed, not derived from the QET Hamiltonian, so every curvature profile inherits an unverified ansatz. And the SNR formula (Eq. 5) is introduced as a model and then treated as if it were a derivation; the appendix simply restates it. The speculative QIX-C section is clearly labeled speculative, so I don't hold that against the main claim, but it doesn't rescue anything either.

What is new is the parametric model and the specific experimental synthesis. It is not new physics. The paper cites Hotta's QET work and its own prior preprint [29]; the quantitative new content is an extension, and [29] is in review, so the evidential base is thin.

I'd send this to a referee only because the question is legitimate and the paper is written in a way that lets a referee pinpoint the errors. But the errors are fatal to the quantitative claims. The author needs to redo the curvature conversion, redo the clock formula, and either derive or explicitly calibrate the stress-energy ansatz before the detectability claims mean anything. As it stands, the paper is not usable as a research preprint.

Recommendation: reject, but with encouragement to resubmit if the first-principles stress-energy computation and corrected units produce a real signal.

Referee Report

4 major / 3 minor

Summary. This paper proposes a tabletop experimental platform, QIX, in which quantum energy teleportation (QET) between entangled detectors creates localized negative energy densities whose semiclassical gravitational backreaction is to be observed with atomic clocks, interferometers, and strain sensors. The manuscript models the negative-energy profile as a Gaussian, converts it to Ricci curvature through a linearized semiclassical relation, defines signal-to-noise ratios and clock-drift observables, and claims that arrays of N ~ 10–100 QET units could yield SNR > 1 and clock signals at the 1e-21 to 1e-17 level. It also introduces a speculative extension, the Quantum-Curvature Compression Channel (QIX-C), as a possible testbed for engineered spacetime curvature.

Significance. If the quantitative claims were correct, the work would present a provocative laboratory route toward testing semiclassical gravity with engineered quantum states. The manuscript is transparent about its modeling assumptions and provides explicit parameter tables and simulation descriptions, which is a strength. However, the central numerical conclusions are undermined by load-bearing errors: a missing 1/c^4 prefactor in the gravitational coupling, a dimensionally inconsistent clock-drift formula, and an SNR model whose claimed derivation is not present. These errors affect the core detectability claims, so the paper in its current form does not support its advertised sensitivity.

major comments (4)

[Appendix B.2, Eq. (B.2); Eq. (13); Eq. (A.3)] The linearized semiclassical relation is applied with the wrong SI prefactor. The Ricci-scalar response to an energy density should be δR = (8πG/c^4)|<T00>|, not δR = 8πG|<T00>|. With the fiducial value ε ~ 1e-11 J/m^3 quoted in Appendix B.4, the resulting curvature is about 2e-54 m^{-2}, roughly 18 orders of magnitude below the claimed δR0 ~ 1e-36 m^{-2}; reaching δR0 would require ε ~ 5e6 J/m^3 rather than a sub-eV-scale density. This error propagates into Eq. (8), Eq. (13), Table 4, and all SNR and clock-detectability claims in Section V.D.
[Eq. (17) / Eq. (A.4)] The clock-drift formula δτ/τ ≈ (1/12)δR L^2 Δt is dimensionally inconsistent: δR L^2 is dimensionless, so multiplying by Δt produces a quantity with units of seconds, while the left-hand side is a dimensionless fractional shift. Inserting the paper's own values (δR ~ 1e-36 m^{-2}, L = 1 mm, Δt = 1 ms) gives about 1e-47 seconds, and restoring the missing 1/c^2 factor still leaves a dimensionless value near 1e-47, not the 1e-21 to 1e-17 signals listed in Table 6. The clock-based feasibility conclusion therefore does not follow from the stated model.
[Section IV / Appendix A.4] The parametric SNR model, Eq. (5), is asserted rather than derived. The text states that a full derivation, including Green's function integration of the semiclassical equations, appears in Appendix A, but Appendix A.4 only restates Eq. (5) without deriving it. No Green's function solution of Eq. (4) is written, and the functional dependences on N/d^3, F/π, and e^{-r} are not obtained from any calculation. Since the SNR contours in Figures 2, 4, and 11 are all generated from Eq. (5), the numerical sensitivity conclusions lack supporting derivation.
[Eq. (3) / Appendix B.1] The Gaussian negative-energy profile <T00(x,t)> ≈ -ε exp(...) is assumed ab initio; it is not computed from the QET interaction Hamiltonian in Eq. (2), the Unruh-DeWitt switching functions, or the detector parameters. Consequently the amplitude ε used in Appendix B.4 is an input to the analysis, not an output of a QET calculation, and every derived curvature profile, SNR contour, and detectability estimate inherits this unverified ansatz. This issue would remain even after correcting the prefactor and dimensional errors above.

minor comments (3)

[Section I / Section IX] There are several typographical errors, including 'Section VIII provides a a speculative extension' and 'In Sections VIII' where the singular is intended.
[Acknowledgments] The sentence 'Computations were performed using Computations and simulations were performed using MATLAB' is garbled and should be corrected.
[References] Reference [29] is listed as 'in review' and is used as a foundation for the present framework; the manuscript should clearly flag that this prior work is not yet available for independent verification.

Circularity Check

3 steps flagged · score 7.0 of 10

The central detectability claim reduces to assumed inputs: δR0 is fixed by a chosen ε in App. B.4, σ_R is chosen in Sec. V.D, and SNR>1 for N~10–100 is then just arithmetic (N δR0/σ_R > 1). The promised derivation of the SNR formula in App. A.4 merely restates the formula.

fitted input called prediction [Sec. V.D (Eq. 9), Sec. V.B (Eq. 8), App. B.4]
""SNR = δR(N)/σ_R" (Eq. 9); "δR(N) ∼ N·δR0" (Eq. 8); "Detection requires SNR>1, achievable with modest arrays of N∼10−100 entangled units using current or near-future technology." App. B.4: "We assume a fiducial energy scale ϵ∼10−11 J/m3, yielding curvature amplitudes δR peak ∼10−36 m−2.""

The detection threshold is computed entirely from two assumed numbers: δR0 is set by choosing ε in App. B.4, and σ_R∼10−35 m−2 is asserted as a 'representative noise floor' in Sec. V.D. With SNR=NδR0/σ_R, the condition SNR>1 becomes N>σ_R/δR0≈10. The advertised N∼10–100 detectability is therefore a restatement of the chosen inputs, not an independently derived prediction. No measurement, external benchmark, or derivation from the QET Hamiltonian fixes these values; changing the assumed ε or σ_R would change the 'prediction' linearly.
other [Sec. IV Eq. (5) and App. A.4]
"Main text: "Full derivation of Eq. 5, including Gaussian modeling of the curvature response and Green’s function integration of the semiclassical Einstein equations, is provided in Appendix Appendix A." Appendix A.4: "These effects combine approximately as: SNR∼... This formula captures the leading parametric dependencies...""

The appendix that is cited as containing the full derivation does not derive the formula: it restates the same equation and adds qualitative remarks about each factor. The SNR law is thus supported by an internal reference that reduces to the formula itself. This is not a derivation from the Gaussian curvature response or Green's functions; it is an asserted ansatz presented as its own justification.

1 more flagged steps

self citation load bearing [Sec. I and Ref. [29]; App. B.1]
""This study builds upon and extends theoretical models introduced in [29], incorporating new signal-to-noise analyses and experimental designs." Ref. [29]: "D. S. Zachary, 'Entanglement-Induced Signatures in Vacuum Energy: Bell, Casimir, and Squeezing Correlations,' Foundations of Physics, in review (2025).""

The theoretical model that underlies the Gaussian negative-energy profile and its magnitude is attributed to the author's own unpublished, in-review paper. No external, machine-checked, or otherwise independent derivation or benchmark is provided for that model. The central curvature amplitude therefore depends on a self-citation chain: [29] provides the model, App. B.1/B.4 supplies the numerical amplitude, Sec. V converts it into a detectability claim. Because [29] is by the same author and not yet published, it does not constitute independent evidence for the load-bearing premise.

full rationale

The paper's central numerical claims are not outputs of a first-principles derivation; they are choices. Appendix B.4 states 'We assume a fiducial energy scale ϵ∼10−11 J/m3, yielding curvature amplitudes δR_peak ∼10−36 m−2,' and Section V.D assumes a noise floor σ_R∼10−35 m−2. With SNR defined as δR(N)/σ_R and δR(N)=N δR0, the claimed N∼10–100 detectability follows by construction from these two inputs. Separately, the relation between ε and δR0 appears arithmetically unsupported even on the paper's own terms: using the stated SI constants, 8πGε is about 10−20 m−2 (and the correct linearized expression adds 1/c^4, giving about 10−54 m−2), not 10−36 m−2; this is a correctness risk that reinforces that δR0 is asserted rather than derived. The SNR formula of Eq. (5) is promised to be derived in Appendix A, but the appendix merely restates it. The self-citation [29], an unpublished in-review paper by the same author, is invoked as the basis of the theoretical model. These elements together make the advertised experimental sensitivity a restatement of assumed parameters rather than a falsifiable prediction; however, the paper does contain independent conceptual content (e.g., QET protocols from Hotta, atomic-clock noise floors, architecture suggestions), so the circularity is substantial but not total. An independent measurement or externally derived value of ε or σ_R would be needed to give the detectability claim predictive content.

Assumptions & free parameters 5 free parameters · 3 assumptions · 1 invented entities

The central claim rests on chosen inputs: Gaussian amplitude epsilon, per-pair curvature delta_R0, and detector noise sigma_R. These are not derived from QET or from instrument specifications. The paper also assumes the semiclassical Einstein equation and a local relation between curvature and energy density. The QIX-C channel is a speculative extension with no independent evidence.

free parameters (5)

epsilon (negative energy density magnitude) = ~1e-11 J/m^3
Chosen fiducial input in Appendix B.4; all curvature amplitudes and SNR results scale with it.
delta_R0 (single-pair curvature) = ~1e-36 m^-2
Stated in Sec. V.B as an estimate from typical QET energy densities; no calculation is shown.
sigma_R (curvature noise floor) = ~1e-35 m^-2
Assumed representative noise in Sec. V.D; not derived from any instrument specification.
G_ent, G_shape, G_multi, G_noise = 2-10, 2-5, 2-3, 1
Dimensionless enhancement multipliers in Eq. (5) set by hand in Tables 3 and 5.
squeezing parameter r and repetition rate f = r = 1.5, f = 1e5 Hz
Chosen simulation parameters in Tables 3 and 5.

assumptions (3)

domain assumption Semiclassical Einstein equation G_mu_nu = 8 pi G <T_mu_nu>
Invoked in Eq. (1) as the source of curvature; its validity for tabletop QET states is the very thing to be tested, not established.
ad hoc to paper Gaussian ansatz for <T00> (Eq. 3)
The energy profile from QET is approximated as a Gaussian with free amplitude and width, not computed from the interaction Hamiltonian in Eq. (2).
ad hoc to paper Local curvature relation delta_R = -8 pi G <T00> (Eq. 13)
Appendix A.2 states this assuming localized negative energy regions dominate curvature changes; it is not the Green's function solution of Eq. (4).

invented entities (1)

Quantum-Curvature Compression Channel (QIX-C)
purpose: A traveling localized curvature dip meant to compress spacetime intervals, presented as an alternative to warp-drive geometries.
Introduced in Sec. VIII as speculative; no falsifiable prediction or quantitative handle beyond the Gaussian pulses that compose it.

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Cite this review

Pith. "Pith review of Entangled Quantum Negative Energy Teleportation as a Probe of Semiclassical Gravity." pith.science (2026). https://pith.science/paper/CCDVSBEQ

@misc{pith2026250619878,
  author       = {Pith},
  title        = {Pith review of: Entangled Quantum Negative Energy Teleportation as a Probe of Semiclassical Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CCDVSBEQ}},
  note         = {Machine review of arXiv:2506.19878}
}

read the original abstract

We investigate the generation of semiclassical spacetime curvature via localized negative energy densities created by quantum energy teleportation (QET) and Casimir-enhanced confinement. Using realistic noise models and experimental architectures, we compute signal-to-noise ratios for detecting the resulting Ricci curvature via atomic clocks, interferometry, and optomechanical strain readout. We propose synchronization and squeezing strategies to enhance detectability and simulate spatial curvature profiles from focused QET pulses. Finally, we introduce a speculative framework -- the Quantum-Curvature Compression Channel -- as an experimentally motivated alternative to warp-drive geometries, enabling apparent geodesic compression through synchronized quantum energy operations. Our results clarify the experimental path toward laboratory tests of exotic stress-energy and semiclassical gravity effects.

Figures

Figures reproduced from arXiv: 2506.19878 by the authors.

**Figure 2.** Contour plot of log10(SNR) as a function of the number of QET units N and detector spacing d. Different curves or surface colors represent varying cavity finesse F values, demonstrating how increased finesse significantly enhances the signal-to-noise ratio. The shaded region below the dashed contour line (SNR = 1) indicates parameter regimes where detection is not feasible with current technology. This visualization… view at source ↗

**Figure 3.** Estimated curvature sensitivity δR versus the number of entangled QET pairs N. The ideal scaling (solid) assumes noiseless additive accumulation. The dashed curve includes thermal and optical noise floors. The shaded region represents a 30% uncertainty band, and the red dotted line denotes a representative detection threshold [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: Log-log scaling of signal-to-noise ratio (SNR) as a function of entangled QET pairs [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: Simulated curvature profiles δR(x) generated by different QET architectures: single pair, unsynchronized array, and synchronized array. Derived from localized Gaussian models of ⟨T00(x)⟩. See Appendix Appendix B for modeling details. VI. Concentrating Negative Energy v…

**Figure 6.** Figure 6: Quantum superposition of two QET channels. Branches [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

**Figure 7.** Figure 7: Temporal and spatial engineering of negative energy. QET pulses can be focused in [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: Fractional clock drift ∆τ/τ as a function of curvature amplitude δR0 for fixed spatial extent L = 1 mm and pulse duration ∆t = 1 ms. The curves indicate the approximate detectability thresholds for optical atomic clocks. D. Strain Detection Analogy The curvature pulses…

**Figure 9.** Figure 9: Strain amplitude h(t) versus curvature amplitude δR for interferometer baselines L = 1 m and L = 10 m. The shaded region denotes the current LIGO sensitivity band for gravitational-wave detection. E. Consolidated Clock Shift Results Combining theoretical and numerical …

**Figure 10.** Figure 10: Simulated fractional clock drift ∆τ/τ versus curvature pulse amplitude δR. Parameters: spatial extent L = 1 mm, pulse duration ∆t = 1 ms. F. Summary QET enables not only the generation of negative energy but also its targeted concentration. Through quantum interferenc…

**Figure 11.** Figure 11: Simulated log-log SNR as a function of QET unit number [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]

**Figure 12.** Figure 12: Schematic of a QIX-C formation from synchronized QET array gates. Each pulse [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]

**Figure 13.** Figure 13: Simulated Ricci curvature profile δR(x, t) from a 1D QET array generating a traveling compression channel. The moving negative curvature dip results from constructive overlap of timed QET-induced stress–energy. Parameters: N = 10, d = 1, σ = 0.5, gate interval = 0.75 …

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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Entanglement-Induced Signatures in Vacuum Energy: Bell, Casimir, and Squeezing Correlations,

D. S. Zachary, “Entanglement-Induced Signatures in Vacuum Energy: Bell, Casimir, and Squeezing Correlations,”Foundations of Physics, in review (2025)

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The warp drive: hyper-fast travel within general relativity,

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doi:10.1088/0264-9381/11/5/001 1994

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Analogue gravity,

C. Barcel´ o, S. Liberati, and M. Visser, “Analogue gravity,” Living Rev. Relativity14, 3 (2011)

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Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,

A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,”Phys. Rev. A69, 062320 (2004)

work page 2004

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Circuit quantum electrodynamics,

A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, “Circuit quantum electrodynamics,” inQuantum Information Processing(Springer, 2021), pp. 1-137

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N. D. Birrell and P. C. W. Davies, *Quantum Fields in Curved Space*, Cambridge University Press, 1982

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A primer on energy conditions,

E. Curiel, “A primer on energy conditions,” in *The Routledge Companion to the Philosophy of Physics*, E. Knox and A. Wilson (eds.), Routledge (2022)

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Quantum gravity: the new synthesis,

B. S. DeWitt, “Quantum gravity: the new synthesis,” in *General Relativity: An Einstein Centenary Survey*, S. W. Hawking and W. Israel (eds.), Cambridge University Press, 1979, pp. 680–745

work page 1979