Pith. sign in

REVIEW 2 major objections 5 minor 93 references

A conducting wire placed near two charged mechanical oscillators changes the distance scaling of their coherent Coulomb coupling from 1/D³ to a much slower 1/(D ln² D), and with continuous position measurement this extends the range over wh

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-01 02:41 UTC pith:5NAOJU4D

load-bearing objection Rigorous first-principles proposal for wire-mediated Coulomb entanglement with a genuinely new scaling law, but the headline distance claims rest on damping and charge values that are not yet demonstrated. the 2 major comments →

arxiv 2607.25341 v1 pith:5NAOJU4D submitted 2026-07-28 quant-ph

Remote entanglement of massive oscillators via wire-mediated Coulomb interaction

Lorenzo Papa , Onur Hosten , Carlos Gonzalez-Ballestero This is my paper
classification quant-ph
keywords Coulomb interactionmechanical oscillatorsentanglementconducting wireimage chargesmacroscopic quantum electrodynamicscontinuous measurementoptomechanics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that image charges induced in a nearby conducting wire fundamentally alter the electrostatic interaction between two charged mechanical oscillators, changing the coherent motional coupling from a 1/D³ free-space decay to a much slower asymptotic 1/(D ln² D) dependence on separation D. For low-frequency oscillators, the wire adds only negligible decoherence, because the imaginary part of the wire response—responsible for loss—is suppressed at low frequencies. Combined with continuous position measurements that purify the mechanical state, this enhanced coupling allows steady-state motional entanglement between milligram-scale oscillators at separations of several hundred microns, a 13.5-fold improvement over free space and potentially up to two orders of magnitude in future systems. If correct, this offers a concrete, near-term route toward entangling massive objects via a fundamental central force, an intermediate step toward gravity-induced entanglement experiments.

Core claim

Using a Green's-function description of the quasi-electrostatic field in the presence of a cylindrical wire, the paper derives the effective two-oscillator dynamics and shows that the wire-mediated coherent coupling is governed by the real part of the scattering Green's function, while the wire-induced decoherence is governed by its imaginary part. For a perfect-conductor limit at oscillator frequencies well below the conductor's relaxation rate, the dominant m = 0 term in the cylindrical multipole expansion yields an asymptotic coupling N12 ≈ q²/(16πϵ₀ m Ω₁ (X_eq)²) · 1/(D ln²(2D/d)), so the total coupling G_tot = 4r(G_fs + N12) decays much more slowly than free space. Because the imaginary

What carries the argument

The central object is the medium-assisted (scattering) Green's function g_M(r, r′, ω) of the electrostatic boundary-value problem, whose real part determines the coherent motional coupling N_jk and whose imaginary part determines the wire-induced decoherence rates Γ_jk. For the cylindrical wire, the Green's function is expanded in cylindrical multipoles; the m = 0 term dominates at large separations and, via a Watson-type asymptotic expansion, gives the 1/(D ln² D) scaling. The second essential ingredient is continuous position measurement, modeled through quantum filtering and Kalman-Bucy equations, which purifies the steady state and enables entanglement.

Load-bearing premise

The predicted entanglement requires an extremely low mechanical damping rate of about 10⁻¹⁰ Hz (quality factor around 2×10¹² at 200 Hz) and a high charge of 3×10⁵ elementary charges per oscillator, values beyond current experimental demonstrations.

What would settle it

Measure the coherent coupling rate G_tot between two charged oscillators separated by D near a cylindrical wire of radius 5 µm at low frequency; if the rate falls faster than D⁻¹ ln⁻²(D) at large D, or if the added decoherence is comparable to intrinsic damping at these frequencies, the predicted long-range entanglement will not appear.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • For milligram-scale oscillators with the parameters of Table I, the observable entanglement range D* is 13.5 times larger than in free space, and the enhancement can approach two orders of magnitude for systems with larger q²/m and higher frequency.
  • The wire-induced decoherence remains negligible at low oscillator frequencies, so the improved range does not come with a significant added noise penalty.
  • A concrete strong-coupling condition, G_tot > 4√2 γ k_B T/(ℏ Ω_f), determines whether steady-state entanglement appears; this can be checked for any proposed experimental parameters.
  • The master-equation framework is valid for arbitrary conductor geometries, so the same formalism can be used to search for geometries that further enhance the coherent coupling.
  • The predicted enhancement relies on the low-frequency suppression of the imaginary part of the wire response; for higher-frequency oscillators the decoherence cost would grow and could limit the effect.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same wire-assisted mechanism could in principle entangle oscillators with different masses or charges, since the coupling rate scales as q²/m; this is not explored in the paper but follows directly from its expressions.
  • The asymptotic 1/(D ln² D) behavior will eventually be overtaken by free-space 1/D³ at very large D, implying a crossover distance that could be measured to test the theory quantitatively.
  • The continuous-measurement purification could be replaced by feedback control to make the entanglement unconditional, which the paper mentions as future work; a reader should interpret the present predictions as conditional on postselecting measurement outcomes.
  • For levitated charged nanoparticles, the same mechanism might operate at even lower frequencies, but the validity of neglecting surface-related electric-field noise at close wire distances remains an experimental question beyond the paper's model.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This paper proposes and analyzes a scheme to enhance the electrostatic interaction between two charged mechanical oscillators by placing them near a cylindrical conducting wire. The authors derive an effective two-oscillator master equation using macroscopic QED, compute the wire-modified coherent coupling and decoherence rates, and show via a Watson-lemma expansion that the coupling asymptotically decays as 1/(D ln^2 D) instead of the free-space 1/D^3. They further show that continuous position measurement can produce steady-state motional entanglement for low-frequency oscillators, and derive approximate formulas for the logarithmic negativity and for the maximum entangling distance. With the parameters in Table I, they predict an entanglement distance of about 800 μm and a 13.5-fold enhancement over free space.

Significance. The formal derivation is the main strength of the paper: the master-equation derivation (App. B), the asymptotic Green's-function expansion (App. D), and the Kalman-filter treatment of the continuous measurement (App. F) are carefully presented, and the analytical approximations are benchmarked against numerical solutions. The predicted change in distance scaling is an original and physically interesting result. However, the experimentally oriented claims rest on parameter values that are not demonstrated simultaneously; the central physics is sound but the headline numbers are conditional. The paper provides a clear framework that can be used to re-evaluate feasibility if the parameter assumptions change.

major comments (2)
  1. [Sec. IIIB / Eq. (32) / Table I] The predicted Dmax ≈ 800 μm and the 13.5× enhancement are controlled by the strong-coupling condition G_tot > 4√2 γ k_B T/(ℏΩ_f). At D ≈ 800 μm, G_tot is only about 0.5 s⁻¹, marginally above the threshold ≈0.36 s⁻¹ set by γ/2π = 10⁻¹⁰ Hz. If the mechanical damping is one order of magnitude larger (γ/2π = 10⁻⁹ Hz), the maximum entangling distance drops by roughly an order of magnitude; if it is 10⁻⁸ Hz, the condition fails at all separations. Neither γ/2π = 10⁻¹⁰ Hz (Q ≈ 2×10¹² at 200 Hz) nor q = 3×10⁵ e has been demonstrated simultaneously on a low-loss mechanical oscillator. The paper should provide a sensitivity analysis D_max(γ, q) and state the simultaneous parameter requirements explicitly.
  2. [Conclusion (final paragraph)] The statement that spurious dielectric surface layers and other surface-induced decoherence channels are negligible is not supported by a quantitative calculation for this geometry. The cited surface-noise studies (Refs. [37,75–77]) concern ion traps and levitated particles at different distances and frequencies. With q = 3×10⁵ e at a surface distance X_min + dx ≈ 4 μm, surface patch potentials or dielectric loss could introduce a motional decoherence channel beyond the ideal Johnson-noise model. Please add an estimate or an upper bound for this contribution, or weaken the 'negligible decoherence' claim to the bulk-conductivity model.
minor comments (5)
  1. [Table I] Table I lists m = 92.5 ng, while the abstract and introduction refer to 'milligram-scale oscillators.' Clarify that m is the effective mass (m = I/L²) of the torsional pendulum, not the physical mass; the current wording is confusing.
  2. [Fig. 4 caption] Typo in the caption: 'Additonally' should be 'Additionally.'
  3. [Fig. 3(a)] The quantum cooperativity C_q is defined only in the text around Fig. 3(a); give an explicit definition in the main text or caption for readability.
  4. [Appendix B, Eq. (B10)] Equation (B10) is lengthy and hard to parse. Consider moving the intermediate Sokhotski-Plemelj step to a short paragraph or supplementary material to improve readability.
  5. [References] Verify bibliographic details for Refs. [43] and [44]; they appear to be recent reports whose journal and volume information may need updating.

Circularity Check

0 steps flagged

No significant circularity: the wire-mediated scaling and entanglement results are derived from first-principles Green's function and open-system equations, with experimental parameters taken as external inputs.

full rationale

The paper's central claims—the 1/(D ln^2 D) coupling scaling and the steady-state entanglement range—are not obtained by fitting or by re-labeling inputs. The effective dynamics (Eqs. (6)-(16)) follow from a standard macroscopic-QED Hamiltonian and Born-Markov tracing; the wire-modified rates N_jk and Gamma_jk are defined from the real/imaginary parts of the scattering Green's function (Eqs. (13)-(14)), which is solved from the Poisson boundary-value problem (Eq. (5)) and evaluated numerically and asymptotically (Appendix D), yielding Eq. (20). The entanglement analysis starts from the derived master-equation rates, adds a continuous position measurement via standard input-output/quantum-filtering theory, and solves the algebraic Riccati equations (Eq. (31)); the analytical approximations (Eqs. (26), (32), (33)) are algebraic consequences of these equations and stated stability/strong-coupling conditions. The maximum distances Dmax and D* are obtained by inverting these expressions, with the detection threshold EN=0.1 explicitly declared "a matter of convention". Table I parameters (including gamma/2pi=1e-10 Hz and q=3e5 e) are experimental/design inputs, not fitted to the target; the sensitivity of the outcome to gamma and q is a correctness/feasibility risk rather than circularity. The only author-overlapping citations ([43,44]) are experimental demonstrations of the milligram torsion pendulums used as parameter baselines; they provide external measured facts and no uniqueness theorem or ansatz is imported from them. No step in the derivation chain reduces by construction to its inputs.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

The paper introduces no new physical entities; it relies on standard macroscopic QED and image-charge concepts. The free parameters are experimental choices or conventions, not circular fits.

free parameters (3)
  • distance to instability dx = min(10^-5 X_min, 1 nm)
    Chosen by hand to model the closest experimentally feasible approach to the wire; directly controls the enhanced coupling and thus the claimed entanglement distance.
  • log-negativity detection threshold = 0.1
    Convention used to define the observable entanglement distance D*; affects the quoted enhancement factor.
  • mechanical damping rate γ/2π = 1e-10 Hz
    Assumed value based on proposed ultra-high-Q torsional oscillators; critically determines the strong-coupling condition and the achievable entanglement distance.
axioms (6)
  • domain assumption Macroscopic quantum electrodynamics framework
    Used to quantize the electromagnetic field in the presence of the lossy wire; standard but an unproved physical framework.
  • domain assumption Electroquasistatic approximation (D << 2πc/Ω0)
    Assumes instantaneous field propagation, valid for the slow oscillators and distances considered.
  • domain assumption Born–Markov master equation for the wire bath
    Assumes weak system-bath coupling and short bath correlation time; requires the spectral density to be linear in ω near the mechanical frequencies.
  • domain assumption High-temperature limit n̄ >> 1
    Used to simplify the dissipators; valid for T=1 K and Ω~200 Hz where n̄ ~ 10⁷.
  • domain assumption Adiabatic elimination of cavity modes (κ >> g)
    Used to derive the effective continuous measurement Hamiltonian; requires bad-cavity regime.
  • standard math Kalman filter for conditional Gaussian dynamics
    The conditional state evolution under homodyne detection is described by classical Kalman–Bucy equations for Gaussian states; standard result in quantum filtering.

pith-pipeline@v1.3.0-alltime-deepseek · 25749 in / 15493 out tokens · 152861 ms · 2026-08-01T02:41:54.480504+00:00 · methodology

0 comments
read the original abstract

We propose a method to enhance Coulomb interaction between charged macroscopic mechanical oscillators by placing a conducting structure in their vicinity. We derive the effective motional dynamics of the two oscillators using macroscopic quantum electrodynamics and show that image charges induced in the conductor fundamentally modify the range of the electrostatic interaction. For the specific case of a cylindrical wire, we predict that the coherent motional coupling changes from the free-space scaling $1/D^3$ to an asymptotic $1/(D\ln^2 D)$ dependence on the separation $D$ between the oscillators, at the cost of only negligible additional decoherence for low-frequency oscillators. We further show that, when combined with continuous position measurements, the enhanced interaction enables the generation of steady-state motional entanglement between the oscillators over significantly larger distances than achievable in free space. For experimentally realistic milligram-scale oscillators, we predict observable entanglement at separations of several hundred microns -- more than an order of magnitude beyond free-space capabilities -- with improvements approaching two orders of magnitude in future systems. These results identify conductor-assisted Coulomb interactions as a resource for quantum control of massive objects and for the exploration of entanglement generated by fundamental central forces.

Figures

Figures reproduced from arXiv: 2607.25341 by Carlos Gonzalez-Ballestero, Lorenzo Papa, Onur Hosten.

Figure 1
Figure 1. Figure 1: FIG. 1. A conducting wire with permittivity [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Characterization of the master equation rates for the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Steady-state entanglement between the two particles [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) All the rates of the master equation as a function of interparticle separation [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

93 extracted references · 13 linked inside Pith

  1. [1]

    Furthermore, we assume the low- frequency limitℏΩ 1 ≪k BT. Under these assumptions the master equation takes the following form: dˆρ dt =− i ℏ h ˆHeff ,ˆρ i +D M[ˆρ] +Dth[ˆρ], (8) where ˆHeff is an effective Hamiltonian,DM describes the wire-induced decoherence, and we include a thermal dis- sipatorD th accounting for the intrinsic damping of each particl...

  2. [2]

    I we obtainD∗/D∗ 0 = 13.5(see the dotted vertical lines in Fig

    For the parameters of Tab. I we obtainD∗/D∗ 0 = 13.5(see the dotted vertical lines in Fig. 3(b)), indicating that the wire enhances the distances at which entanglement can be observed by more than an order of magnitude. To generalize our result to a wider range of param- eters, we display in Fig. 3(d) the enhancement of the entanglement range,D ∗/D∗ 0, as...

  3. [3]

    Aspelmeyer, T

    M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys.86, 1391 (2014)

    2014

  4. [4]

    W. P. Bowen and G. J. Milburn,Quantum Optomechan- ics(CRC Press, 2015)

    2015

  5. [5]

    C. M. DeWitt and D. Rickles,The Role of Gravitation in Physics: Report from the 1957 Chapel Hill Conference (Edition Open Access, 2011)

    1957

  6. [6]

    Marletto and V

    C. Marletto and V. Vedral, Gravitationally Induced En- tanglement between Two Massive Particles is Sufficient EvidenceofQuantumEffectsinGravity,PhysicalReview Letters119, 240402 (2017)

    2017

  7. [7]

    Belenchia, R

    A. Belenchia, R. M. Wald, F. Giacomini, E. Castro-Ruiz, Č. Brukner, and M. Aspelmeyer, Quantum superposition of massive objects and the quantization of gravity, Phys- ical Review D98, 126009 (2018)

    2018

  8. [8]

    S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroš, M. Paternostro, A. A. Geraci, P. F. Barker, M. S. Kim, and G. Milburn, Spin Entanglement Wit- ness for Quantum Gravity, Physical Review Letters119, 240401 (2017)

    2017

  9. [9]

    Christodoulou, A

    M. Christodoulou, A. Di Biagio, M. Aspelmeyer, Č. Brukner, C. Rovelli, and R. Howl, Locally Mediated Entanglement in Linearized Quantum Gravity, Physical Review Letters130, 100202 (2023)

    2023

  10. [10]

    Martín-Martínez and T

    E. Martín-Martínez and T. R. Perche, What gravity me- diated entanglement can really tell us about quantum gravity, Physical Review D108, L101702 (2023)

    2023

  11. [11]

    Bengyat, A

    O. Bengyat, A. Di Biagio, M. Aspelmeyer, and M. Christodoulou, Gravity-mediated entanglement be- tween oscillators as quantum superposition of geometries, Physical Review D110, 056046 (2024)

    2024

  12. [12]

    Aspelmeyer, Quantum entanglement by gravity as tests of gravitational collapse modelsà laDiósi and Pen- rose, Comptes Rendus

    M. Aspelmeyer, Quantum entanglement by gravity as tests of gravitational collapse modelsà laDiósi and Pen- rose, Comptes Rendus. Physique27, 1 (2026)

    2026

  13. [13]

    C. F. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, M. Asjad, A. A. Clerk, F. Massel, M. J. Woolley, and M. A. Sillanpää, Stabilized entangle- ment of massive mechanical oscillators, Nature556, 478 (2018)

    2018

  14. [14]

    Riedinger, A

    R. Riedinger, A. Wallucks, I. Marinković, C. Löschnauer, M. Aspelmeyer, S. Hong, and S. Gröblacher, Remote quantum entanglement between two micromechanical os- cillators, Nature556, 473 (2018)

    2018

  15. [15]

    E. A. Wollack, A. Y. Cleland, R. G. Gruenke, Z. Wang, P. Arrangoiz-Arriola, and A. H. Safavi-Naeini, Quan- tum state preparation, tomography, and entanglement of mechanical oscillators, Nature604, 463 (2022), arXiv:2110.07561 [quant-ph]. 10

    Pith/arXiv arXiv 2022

  16. [16]

    Kotler, G

    S. Kotler, G. A. Peterson, E. Shojaee, F. Lecocq, K. Ci- cak, A.Kwiatkowski, S.Geller, S.Glancy, E.Knill, R.W. Simmonds, J. Aumentado, and J. D. Teufel, Direct ob- servation of deterministic macroscopic entanglement, Sci- ence372, 622 (2021)

    2021

  17. [17]

    Hosten, Constraints on probing quantum coherence to infer gravitational entanglement, Physical Review Re- search4, 013023 (2022)

    O. Hosten, Constraints on probing quantum coherence to infer gravitational entanglement, Physical Review Re- search4, 013023 (2022)

    2022

  18. [18]

    Aspelmeyer, How to avoid the appearance of a classical world in gravity experiments (2022), arXiv:2203.05587 [quant-ph]

    M. Aspelmeyer, How to avoid the appearance of a classical world in gravity experiments (2022), arXiv:2203.05587 [quant-ph]

    Pith/arXiv arXiv 2022

  19. [19]

    Bulling, M

    J. Bulling, M. O. E. Steiner, J. S. Pedernales, and M. B. Plenio, Stability Thresholds for Gravitation- ally Induced Entanglement in Shielded Setups (2026), arXiv:2604.22593 [quant-ph]

    Pith/arXiv arXiv 2026

  20. [20]

    Q. Wu, Y. Xiao, and Z.-M. Zhang, Stationary entan- glement between two nanomechanical oscillators induced by Coulomb interaction*, Chinese Physics B25, 014203 (2015)

    2015

  21. [21]

    Qvarfort, S

    S. Qvarfort, S. Bose, and A. Serafini, Mesoscopic entan- glement through central–potential interactions, J. Phys. B: At. Mol. Opt. Phys.53, 235501 (2020)

    2020

  22. [22]

    Sohail, R

    A. Sohail, R. Ahmed, C. S. Yu, and T. Munir, Enhanced entanglement induced by Coulomb interaction in cou- pled optomechanical systems, Physica Scripta95, 035108 (2020)

    2020

  23. [23]

    Cosco, J

    F. Cosco, J. S. Pedernales, and M. B. Plenio, Enhanced force sensitivity and entanglement in periodically driven optomechanics, Phys. Rev. A103, L061501 (2021)

    2021

  24. [24]

    Rudolph, U

    H. Rudolph, U. Delić, M. Aspelmeyer, K. Hornberger, and B. A. Stickler, Force-Gradient Sensing and Entangle- ment via Feedback Cooling of Interacting Nanoparticles, Phys. Rev. Lett.129, 193602 (2022), arXiv:2204.13684 [quant-ph]

    Pith/arXiv arXiv 2022

  25. [25]

    Li and Z

    G. Li and Z. Yin, Entangling two levitated charged nanospheres through Coulomb interaction, Chinese Physics B33, 074205 (2024)

    2024

  26. [26]

    Deplano, A

    Q. Deplano, A. Pontin, A. Ranfagni, F. Marino, and F. Marin, Coulomb coupling between two nanospheres trappedin a bichromatic optical tweezer,Optica11, 1773 (2024), arXiv:2408.02597 [physics.optics]

    Pith/arXiv arXiv 2024

  27. [27]

    Winkler, A

    K. Winkler, A. V. Zasedatelev, B. A. Stickler, U. Delić, A. Deutschmann-Olek, and M. Aspelmeyer, Steady-state entanglement of interacting masses in free space through optimal feedback control (2025), arXiv:2408.07492 [quant-ph]

    arXiv 2025

  28. [28]

    A. N. Poddubny, K. Winkler, B. A. Stickler, U. Delić, M. Aspelmeyer, and A. V. Zasedatelev, Nonequilibrium entanglement between levitated masses under optimal control (2025), arXiv:2408.06251 [quant-ph]

    Pith/arXiv arXiv 2025

  29. [29]

    Horovitz and A

    G. Horovitz and A. N. Poddubny, Parametric resonant enhancement of motional entanglement under optimal control: An analytical study, Physical Review A113, 053521 (2026)

    2026

  30. [30]

    S. Dey, P. Barker, and A. Datta, Testing Sponta- neous Collapse Models with Coulomb Mediated Squeez- ing (2026), arXiv:2604.21705 [quant-ph]

    Pith/arXiv arXiv 2026

  31. [31]

    Fröwis, P

    F. Fröwis, P. Sekatski, W. Dür, N. Gisin, and N. San- gouard,Macroscopicquantumstates: Measures, fragility, and implementations, Reviews of Modern Physics90, 025004 (2018)

    2018

  32. [32]

    J. R. Zurita-Sánchez and C. Henkel, Lossy electrical transmission lines: Thermal fluctuations and quantiza- tion, Physical Review A73, 063825 (2006)

    2006

  33. [33]

    Daniilidis, T

    N. Daniilidis, T. Lee, R. Clark, S. Narayanan, and H. Häffner, Wiring up trapped ions to study aspects of quantum information, J. Phys. B: At. Mol. Opt. Phys. 42, 154012 (2009)

    2009

  34. [34]

    D. An, A. M. Alonso, C. Matthiesen, and H. Häffner, Coupling Two Laser-Cooled Ions via a Room- Temperature Conductor, Physical Review Letters 128, 063201 (2022)

    2022

  35. [35]

    Q. Yu, A. M. Alonso, J. Caminiti, K. M. Beck, R. T. Sutherland, D. Leibfried, K. J. Rodriguez, M. Dhital, B. Hemmerling, and H. Häffner, Feasibility study of quantum computing using trapped electrons, Physical Review A105, 022420 (2022)

    2022

  36. [36]

    N. V. Horne and M. Mukherjee, Coupling the motional quantum states of spatially distant ions using a conduct- ing wire (2021), arXiv:2111.14957 [quant-ph]

    Pith/arXiv arXiv 2021

  37. [37]

    B. Yu, R. Betzholz, and J. Cai, Strong coherent ion- electron coupling using a wire data bus, Phys. Rev. Appl. 22, 024032 (2024)

    2024

  38. [38]

    S. Y. Buhmann,Dispersion Forces I: Macroscopic Quantum Electrodynamics and Ground-State Casimir, Casimir–Polder and van Der Waals Forces, Springer Tracts in Modern Physics, Vol. 247 (Springer, Berlin, Heidelberg, 2012)

    2012

  39. [39]

    Martinetz, K

    L. Martinetz, K. Hornberger, and B. A. Stickler, Surface- Induced Decoherence and Heating of Charged Particles, PRX Quantum3, 030327 (2022)

    2022

  40. [40]

    Jakubec, C

    C. Jakubec, C. Jarzynski, and K. Sinha, Decoherence and Brownianmotionofapolarizableparticlenearamedium, Physical Review A112, 042225 (2025)

    2025

  41. [41]

    Izadyari, O

    M. Izadyari, O. Pusuluk, K. Sinha, and Ö. E. Müste- caplıoğlu, Steady-State Entanglement Generation via Casimir-Polder Interactions, Scientific Reports15, 37105 (2025), arXiv:2406.02270 [quant-ph]

    arXiv 2025

  42. [42]

    M. R. Vanner, J. Hofer, G. D. Cole, and M. Aspelmeyer, Cooling-by-measurement and mechanical state tomogra- phy via pulsed optomechanics, Nature Communications 4, 2295 (2013)

    2013

  43. [43]

    D. Miki, N. Matsumoto, A. Matsumura, T. Shichijo, Y. Sugiyama, K. Yamamoto, and N. Yamamoto, Gen- erating quantum entanglement between macroscopic ob- jects with continuous measurement and feedback control, Phys. Rev. A107, 032410 (2023)

    2023

  44. [44]

    D. Miki, A. Matsumura, and K. Yamamoto, Feasible generation of gravity-induced entanglement by using op- tomechanical systems (2024), arXiv:2406.04361 [quant- ph]

    arXiv 2024

  45. [45]

    Agafonova, U

    S. Agafonova, U. Mishra, F. Diorico, and O. Hosten, Zigzag optical cavity for sensing and controlling torsional motion, Physical Review Research6, 013141 (2024)

    2024

  46. [46]

    Agafonova, P

    S. Agafonova, P. Rosselló, M. Mekonnen, and O. Hosten, One-milligram torsional pendulum toward experiments at the quantum-gravity interface, Communications Physics9, 80 (2026)

    2026

  47. [47]

    Barzanjeh, A

    S. Barzanjeh, A. Xuereb, S. Gröblacher, M. Paternostro, C. A. Regal, and E. M. Weig, Optomechanics for quan- tum technologies, Nat. Phys.18, 15 (2022)

    2022

  48. [48]

    Barcellona, R

    P. Barcellona, R. Bennett, and S. Y. Buhmann, Manipu- lating the Coulomb interaction: A Green’s function per- spective, J. Phys. Commun.2, 035027 (2018)

    2018

  49. [49]

    Martinetz, K

    L. Martinetz, K. Hornberger, J. Millen, M. S. Kim, and B. A. Stickler, Quantum electromechanics with levitated nanoparticles, npj Quantum Inf6, 101 (2020)

    2020

  50. [50]

    Winstone, R

    G. Winstone, R. Bennett, M. Rademacher, M. Rashid, 11 S. Buhmann, and H. Ulbricht, Direct measurement of the electrostatic image force of a levitated charged nanopar- ticle close to a surface, Physical Review A98, 053831 (2018)

    2018

  51. [51]

    Schlosshauer, Quantum decoherence, Physics Reports 831, 1 (2019)

    M. Schlosshauer, Quantum decoherence, Physics Reports 831, 1 (2019)

    2019

  52. [52]

    Gonzalez-Ballestero, P

    C. Gonzalez-Ballestero, P. Maurer, D. Windey, L. Novotny, R. Reimann, and O. Romero-Isart, Theory for cavity cooling of levitated nanoparticles via coherent scattering: Master equation approach, Physical Review A100, 013805 (2019)

    2019

  53. [53]

    Gonzalez-Ballestero, J

    C. Gonzalez-Ballestero, J. Zielińska, M. Rossi, A. Mil- itaru, M. Frimmer, L. Novotny, P. Maurer, and O. Romero-Isart, Suppressing Recoil Heating in Levi- tated Optomechanics Using Squeezed Light, PRX Quan- tum4, 030331 (2023)

    2023

  54. [54]

    Breuer and F

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

    2002

  55. [55]

    D. F. Walls and G. J. Milburn,Quantum Optics, Grad- uate Texts in Physics (Springer Nature Switzerland, Cham, 2025)

    2025

  56. [56]

    This dissipator can be derived by tracing out an indepen- dent bath of harmonic oscillators, but within the Born- Markov approximation it is justified to simply add it to the master equation as we have done here [87]

  57. [57]

    J. D. Jackson,Classical Electrodynamics(John Wiley & Sons, 2021)

    2021

  58. [58]

    S. T. Cui, Electrostatic potential in cylindrical dielectric media using the image charge method, Mol. Phys.104, 2993 (2006)

    2006

  59. [59]

    Eberlein and R

    C. Eberlein and R. Zietal, Force on a neutral atom near conducting microstructures, Phys. Rev. A75, 032516 (2007)

    2007

  60. [60]

    Ludwig, K

    M. Ludwig, K. Hammerer, and F. Marquardt, Entangle- ment of mechanical oscillators coupled to a nonequilib- rium environment, Physical Review A82, 012333 (2010)

    2010

  61. [61]

    Tokarska and A

    J. Tokarska and A. Dragan, Gravitationally Induced En- tanglement Between Particles in Harmonic Traps: Limits for Gaussian States (2025), arXiv:2512.24312 [quant-ph]

    arXiv 2025

  62. [62]

    Vidal and R

    G. Vidal and R. F. Werner, Computable measure of en- tanglement, Physical Review A65, 032314 (2002)

    2002

  63. [63]

    (CRC Press, Boca Raton, 2023)

    Alessio Serafini,Quantum Continuous Variables: A Primer of Theoretical Methods, 2nd ed. (CRC Press, Boca Raton, 2023)

    2023

  64. [64]

    L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, In- separability Criterion for Continuous Variable Systems, Phys. Rev. Lett.84, 2722 (2000)

    2000

  65. [65]

    Simon, Peres-Horodecki Separability Criterion for Continuous Variable Systems, Phys

    R. Simon, Peres-Horodecki Separability Criterion for Continuous Variable Systems, Phys. Rev. Lett.84, 2726 (2000)

    2000

  66. [66]

    N. J. Simon, E. S. Drexler, and R. P. Reed,Properties of Copper and Copper Alloys at Cryogenic Temperatures, Tech. Rep. NIST MONO 177 (National Institute of Stan- dards and Technology, Gaithersburg, MD, 1992)

    1992

  67. [67]

    T. P. Purdy, R. W. Peterson, and C. A. Regal, Observa- tion of Radiation Pressure Shot Noise on a Macroscopic Object, Science339, 801 (2013), arXiv:1209.6334 [quant- ph]

    Pith/arXiv arXiv 2013

  68. [68]

    Rossi, D

    M. Rossi, D. Mason, J. Chen, Y. Tsaturyan, and A. Schliesser, Measurement-based quantum con- trol of mechanical motion, Nature563, 53 (2018), arXiv:1805.05087 [quant-ph]

    Pith/arXiv arXiv 2018

  69. [69]

    Delić, M

    U. Delić, M. Reisenbauer, K. Dare, D. Grass, V. Vuletić, N. Kiesel, and M. Aspelmeyer, Motional Quantum Ground State of a Levitated Nanoparticle from Room Temperature, Science367, 892 (2020), arXiv:1911.04406 [quant-ph]

    Pith/arXiv arXiv 2020

  70. [70]

    Piotrowski, D

    J. Piotrowski, D. Windey, J. Vijayan, C. Gonzalez- Ballestero, A. d. l. R. Sommer, N. Meyer, R. Quidant, O. Romero-Isart, R. Reimann, and L. Novotny, Simulta- neous ground-state cooling of two mechanical modes of a levitated nanoparticle, Nature Physics19, 1009 (2023), arXiv:2209.15326 [quant-ph]

    Pith/arXiv arXiv 2023

  71. [71]

    Dania, O

    L. Dania, O. S. Kremer, J. Piotrowski, D. Candoli, J. Vijayan, O. Romero-Isart, C. Gonzalez-Ballestero, L. Novotny, and M. Frimmer, High-purity quantum op- tomechanics at room temperature, Nature Physics21, 1603 (2025)

    2025

  72. [72]

    S. C. Edwards and V. P. Belavkin, Optimal Quan- tum Filtering and Quantum Feedback Control (2005), arXiv:quant-ph/0506018

    Pith/arXiv arXiv 2005

  73. [73]

    H. M. Wiseman and G. J. Milburn,Quantum Measure- ment and Control(Cambridge University Press, Cam- bridge, 2009)

    2009

  74. [74]

    R. E. Kalman and R. S. Bucy, New Results in Linear Filtering and Prediction Theory, J. Basic Eng83, 95 (1961)

    1961

  75. [75]

    (33) can be neglected

    This can be derived by noting that in this limit, the factorπ 2/4in Eq. (33) can be neglected. This enables to write its analytical solution asD max = (d/2) exp h 2W p (D0max)3/d/(2X equ 1 ) i withW(z)the Lambert W function. At low values of decoherenceγ¯n, the factorD 0 max tends to infinity and one can use the asymptotic expansionW(z)∼ln(z). This yields...

  76. [76]

    J. R. Zurita-Sánchez and C. Henkel, Wiring up single electron traps to perform quantum gates, New Journal of Physics10, 083021 (2008)

    2008

  77. [77]

    Brownnutt, M

    M. Brownnutt, M. Kumph, P. Rabl, and R. Blatt, Ion- trap measurements of electric-field noise near surfaces, Reviews of Modern Physics87, 1419 (2015)

    2015

  78. [78]

    Kumph, C

    M. Kumph, C. Henkel, P. Rabl, M. Brownnutt, and R. Blatt, Electric-field noise above a thin dielectric layer on metal electrodes, New Journal of Physics18, 023020 (2016)

    2016

  79. [79]

    J. A. Sedlacek, A. Greene, J. Stuart, R. McConnell, C. D. Bruzewicz, J. M. Sage, and J. Chiaverini, Distance scal- ing of electric-field noise in a surface-electrode ion trap, Physical Review A97, 020302 (2018)

    2018

  80. [80]

    Kilianski and R

    R. Kilianski and R. Bennett, Atoms near a conducting wedge: Decay rates and entanglement around a corner, Physical Review A110, 062812 (2024)

    2024

Showing first 80 references.