Genuine quantum non-Gaussianity and metrological sensitivity of Fock states prepared in a mechanical resonator

Igor Kladari\'c; Luk\'a\v{s} Lachman; Matteo Fadel; Max-Emanuel Kern; Q. Rumman Rahman; Radim Filip; Yiwen Chu

REVIEW 2 major objections 6 minor 1 cited by

Genuine quantum non-Gaussianity and metrological sensitivity of Fock states prepared in a mechanical resonator

T0 review · 2 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read The paper reports preparation of mechanical Fock states up to |6> with genuine quantum non-Gaussianity and a displacement sensitivity exceeding that of an ideal Fock |3> state.

desk verdict A solid cQAD advance: genuine QNG up to n=6 and a loss-adjusted metrological benchmark, but both claims sit on one model-dependent readout that deserves scrutiny. read the letter →

arxiv 2412.20971 v3 pith:VFLNXNHP submitted 2024-12-30 quant-ph

Q. Rumman Rahman , Igor Kladarić , Max-Emanuel Kern , Lukáš Lachman , Yiwen Chu , Radim Filip , Matteo Fadel This is my paper · ORCID

classification quant-ph

keywords Fockstatesmechanicalresonatorquantumnon-GaussianityFisherinformationdisplacementsensingoptimalcontrolHBARcircuitacoustodynamics

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 reports the preparation of high-number Fock states, phonon number states of a mechanical resonator, in a high-overtone bulk acoustic wave resonator coupled to a superconducting qubit. The states are produced by microwave pulses optimized with quantum optimal control, and the paper's central claim is that the resulting states show genuine quantum non-Gaussianity up to the six-phonon level: they cannot be written as Gaussian operations (displacements and squeezing) applied to superpositions with at most five phonons. The paper further introduces a loss-adjusted metrological hierarchy based on the quantum Fisher information and shows that the experimentally realized $|6\rangle$ state, even after energy relaxation and readout imperfections, has a displacement sensitivity exceeding that of an ideal Fock $|3\rangle$ state. If correct, this establishes optimal control as a practical route to multiphonon non-Gaussian mechanical states and connects their non-Gaussian character directly to a sensing advantage.

What carries the argument

The argument runs on three mechanisms. The first is the resonant-interaction phonon number (RPN) measurement, which initializes the qubit in its excited state, lets it interact with the phonon mode for a variable time, and fits the resulting qubit population oscillations to master-equation basis functions to extract the phonon number distribution $P_n$. The second is the genuine quantum non-Gaussianity criterion $F_{a,n}(\rho) = P_n + a P_{n+1}$, whose threshold $F_n(a)$ is the maximum of this functional over all states of the form a displaced and squeezed mixture of Fock states up to $|n-1\rangle$; exceeding the threshold for any $a$ certifies genuine $n$-phonon QNG, and the use of $P_{n+1}$ makes the test robust to loss. The third is the quantum Fisher information for displacement sensing: an ideal Fock state $|n\rangle$ gives $F_Q = 4(2n+1)$, and the paper computes the classical Fisher information from Fock-basis populations after an amplitude-damping channel, producing a loss-adjusted hierarchy that ranks the prepared states against ideal Fock states under the same decoherence.

What would settle it

A direct check is to reconstruct the same prepared states with an independent measurement, such as displaced-parity Wigner tomography, and compare the resulting phonon number distribution and Fisher information with the RPN-based values; if the independent reconstruction disagrees with the RPN fits beyond the reported uncertainties, or if calibrating the RPN basis on known coherent states changes the extracted $P_n$ values significantly, the central claim would be falsified. A second check would be to prepare a known state (e.g., a coherent state) and verify that the RPN analysis recovers its expected distribution and Fisher information.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes three linked results. First, quantum-optimal-control pulses of a few microseconds prepare Fock states $|1\rangle$ through $|7\rangle$ in the acoustic resonator, with measured fidelities above 75% for states up to $|6\rangle$. Second, a hierarchical criterion for genuine quantum non-Gaussianity—built from the probabilities $P_n$ and $P_{n+1}$ of detecting $n$ and at least $n+1$ phonons, with thresholds optimized over displaced, squeezed mixtures of states with at most $n-1$ phonons—is violated for $n = 1,\dots,6$, so the prepared states cannot be generated by any Gaussian transformation on states containing up to five phonon contributions. Third, when the amplitude-damping channel of the measurement is included in the comparison, the classical Fisher information of the prepared $|6\rangle$ state for estimating a displacement amplitude exceeds that of an ideal Fock $|3\rangle$ state subjected to the same loss, implying a quantum-enhanced force sensitivity beyond the classical limit of $63.2\ \mathrm{fN}/\sqrt{\mathrm{Hz}}$ for the device.

Load-bearing premise

The conclusions rest on the assumption that the resonant-interaction phonon number measurement returns unbiased estimates of the phonon number distribution $P_n$; if the master-equation basis functions mis-model the readout—through an uncalibrated coupling strength, qubit leakage, or a decay channel that is not simple amplitude damping—the extracted $P_n$ values could shift enough to change the QNG certification or the comparison with ideal Fock states.

Editorial extensions

If this is right

Fock states up to $|6\rangle$ can be prepared in a mechanical resonator with fidelity exceeding 75% using optimal-control pulses shorter than the decoherence time.
Genuine quantum non-Gaussianity is certified for $n = 1$ to $6$, so the prepared states cannot be produced by Gaussian operations on states with fewer phonons, even when the criterion allows for losses.
The prepared $|6\rangle$ state, measured through the device's lossy readout, has a higher Fisher information for displacement amplitude than an ideal Fock $|3\rangle$ state under the same amplitude-damping channel.
Each prepared state can tolerate a quantifiable amount of loss—measured both by simulated free evolution and by an equivalent beamsplitter—before it stops violating its QNG threshold, with higher Fock states losing certification sooner.
For this device, the sensitivity advantage translates into a quantum-enhanced force sensitivity beyond the classical limit of $63.2\ \mathrm{fN}/\sqrt{\mathrm{Hz}}$.

Reading between the lines

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

The loss-adjusted Fisher hierarchy is a platform-independent benchmark: any bosonic mode with a known $T_1$ can be ranked against ideal Fock states under the same damping channel, so the comparison method should transfer to microwave cavities, trapped ions, and optical systems without modification.
Because the $P_n/P_{n+1}$ QNG criterion can be violated even for states with modest fidelity and purity, it offers a practical acceptance test for non-Gaussian resources in hybrid devices, complementing Wigner-function negativity measurements.
A testable extension suggested by the method: shortening the RPN readout time (through stronger coupling or a quantum non-demolition measurement) should increase both the highest certifiable Fock number and the metrological advantage, since less amplitude damping would occur during readout.
The same optimal-control preparation could be directed at superposition states such as $|0\rangle + |n\rangle$ or at two-mode number-difference states, where the Fisher hierarchy would need to be recomputed for the corresponding multi-mode displacement generator.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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,

What you should know first: this is a real experimental step forward. The group prepared Fock states in an HBAR using optimal control, kept measured fidelity above 75% up to n=6, and certified genuine quantum non-Gaussianity at n=6 against an external, parameter-free threshold built on Pn + a Pn+1. They also go beyond the usual ideal-QFI comparison: they model the measurement as amplitude damping with an independently measured T1 and show the prepared n=6 state beats an ideal |3> Fock state under that same lossy channel. That is a more honest metrological benchmark than what most papers in this area offer.

The QNG criterion extension is useful, the tau_n = tau_1/n consistency check is reassuring, and the Wigner reconstruction agreeing with simulation is a good sanity check. I also appreciate that the QNG thresholds come from prior literature rather than being fit to the data.

The soft spot is exactly what the stress-test note flags. Both headline claims are computed from the phonon-number distribution Pn extracted by fitting RPN traces to master-equation basis functions. An unmodeled qubit leakage channel, a detuning error, a second near-degenerate mode, or a measurement-induced dephasing term could bias Pn. The n=6 QNG violation and the FI edge over the lossy |3> state are not huge margins, so a modest redistribution of Pn could move either result. The paper gives internal consistency checks, but those validate the decoherence rates, not the absolute Pn scale that sets both thresholds. There is also no raw data or code released, and the uncertainty bars on {Pn, Pn+1} appear to be fit-only, so systematic effects are not quantified. Minor point: the abstract's fidelity sentence reads as if all measured states exceed 75%, which Fig. 1(a) presumably clarifies, but it would be cleaner to state the number as measured and not simulated.

That said, I do not think these concerns are fatal. The thresholds are external, T1 is independent, and the internal physics checks behave as expected. The right fix is a frank systematic-error analysis of the RPN readout, plus data release. This paper deserves a serious referee, and I would send it out without hesitation.

For you: worth reading for the QNG criterion and the loss-adjusted metrology, but keep an eye on the RPN model as the single point of failure.

Referee Report

2 major / 6 minor

Summary. This manuscript reports the preparation of Fock states up to |6> in a high-overtone bulk acoustic wave resonator coupled to a superconducting qubit, using quantum optimal control. The states are characterized through resonant-interaction phonon-number (RPN) measurements, and the resulting phonon-number distributions are used to evaluate a robust genuine quantum non-Gaussianity criterion from the literature. The measured {P_n, P_{>= n+1}} points are reported to violate the QNG thresholds for n=1,...,6, and the loss tolerance of the violations is quantified. The same measured distributions are used to compute the classical Fisher information for displacement-amplitude estimation, which is compared with ideal Fock states and with ideal Fock states after an amplitude-damping channel representing measurement loss; from this comparison the authors conclude that the prepared n=6 state has displacement sensitivity better than an ideal Fock |3> state under the same lossy readout. The theoretical tools are previously established, and the experimental platform is described in detail.

Significance. If the central claims are fully supported, this is a significant experimental result: it demonstrates high-order Fock states in a mechanical oscillator, certified by externally defined QNG thresholds rather than by Wigner negativity alone, and it provides a Fisher-information-based metrological benchmark that connects non-Gaussianity to sensing performance. Strengths of the manuscript include the use of parameter-free QNG thresholds, an independently measured phonon T1 in the loss model, the internal consistency of the measured decay times tau_n = tau_1/n with T1, and the explicit inclusion of readout-induced relaxation in the simulations. The principal risk is that both headline claims—the n=6 QNG violation and the metrological advantage over an ideal lossy Fock |3>—are computed from the same model-dependent RPN reconstruction of the phonon-number distribution; the report therefore focuses on validating that reconstruction.

major comments (2)

[Methods: RPN measurement; Supplement Fig. 8 and Sec. V] The QNG violation for n=6 in Fig. 2(a) and the displacement-sensitivity comparison in Fig. 3(a) are both computed from the phonon-number distribution {P_n} extracted by fitting RPN traces to master-equation basis functions. The manuscript does not provide a systematic-error analysis of this fit: no residuals, no calibration of the coupling g, no explicit test for qubit leakage, spurious near-degenerate modes, detuning errors, or readout assignment errors. Because the n=6 point sits close to a high-n threshold and the FI advantage over the ideal lossy |3> state is a modest margin, an unmodeled readout imperfection could shift the extracted Pn enough to affect both headline conclusions. Please add a systematic-error budget for the fitted {P_n} and an independent cross-check of the absolute scale of the distribution—for example, comparing RPN results with Wigner-tomography-based populations for at least the n=5 and n=6 states—so that the model dependence is demonstrated to be under control.
[Fig. 2(a); Supplement Fig. 8] The claimed QNG violations are presented graphically without the corresponding numerical values and confidence levels. The supplement states that the error bars come from fitting-function uncertainties, which are statistical only, and the threshold curves become increasingly tight at higher n. Please report the measured {P_n, P_{>= n+1}} values with their statistical and systematic uncertainties for each n and state explicitly the significance (e.g., number of standard deviations) of each threshold violation, in particular for n=6. This information is necessary to establish that the n=6 violation is not an artifact of the fit uncertainties.

minor comments (6)

[Notation throughout; Fig. 2(a)] Notation: P_{n+1} is used both for the single Fock probability and for the tail probability P_{>= n+1}; please introduce a distinct symbol, e.g., P_{>= n+1}, and use it in the text and in the axes of Fig. 2(a).
[Supplement Eq. (25)] Supplement Eq. (25): the left-hand side should be Delta F_0 sqrt(T) (or an equivalent statement of the sensitivity in N/sqrt(Hz)), not Delta F_0 sqrt(1/t_cycle); as printed the equation is dimensionally inconsistent.
[Fig. 2(d)] The two methods used in Fig. 2(d) to quantify QNG depth are the same amplitude-damping model expressed as a wait time and as a beamsplitter transmittance; calling them 'independent' is inaccurate.
[Abstract; Fig. 3(a)] The abstract and Fig. 3(a) should clarify that the post-loss hierarchy is the classical Fisher information for Fock-basis population measurements, not the quantum Fisher information of the lossy states; Fock-basis measurements are optimal only for the ideal pure Fock states.
[Fig. 1(a) caption] The caption of Fig. 1(a) should define what is meant by 'fidelity' for each of the four curves (optimizer target, simulated prepared state, simulated measured state, and experimentally measured fidelity).
[Data availability in main text] Please include a numerical table of the experimental Pn values and the maximum FI values in the main text or supplement, to allow readers to reproduce Figs. 2 and 3 without reading values off the plots.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: QNG thresholds and the Fisher-information hierarchy are parameter-free and rely on independently measured T1; the RPN reconstruction model is a measurement robustness risk, not a circular reduction.

full rationale

The derivation chain is self-contained. The two headline claims—genuine n-phonon QNG up to n=6 and displacement sensitivity exceeding that of an ideal lossy Fock |3>—are both evaluated by comparing experimentally extracted phonon-number probabilities {Pn} against parameter-free theoretical curves. The QNG thresholds Fn(a) are obtained by maximizing the functional Fa,n(ρ)=Pn+aP_{n+1} over the convex hull of Gaussian-displaced-and-squeezed superpositions of Fock states up to |n−1>; no parameter of the threshold is fitted to the measured data. Although the robust-QNG functional and earlier QNG criteria are cited from the same author group (Refs [16–18,26]), they are published theoretical results with stated assumptions that do not include the present experimental data, so they constitute independent support rather than circular input. The metrological claim similarly uses the standard quantum Cramér–Rao bound and classical Fisher information, with the lossy-ideal-Fock hierarchy computed analytically from the independently measured T1 via an amplitude-damping channel; the comparison point for |3> is not fitted to the measured state. The only model dependence—the RPN master-equation basis used to infer {Pn}—is a measurement-model fidelity assumption. A mis-modeled readout could shift the inferred distribution and move points across a threshold, but that is a correctness or robustness risk, not a circular reduction: the thresholds and the loss hierarchy are not defined in terms of the fitted Pn. No equation in the paper is equivalent to its own input by construction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claims rest on the QNG criterion from prior literature as an external benchmark, on the master-equation decoherence model with measured rates, and on the RPN reconstruction of Pn from qubit population fits. No new physical entities are introduced. The only fitted quantities are control-pulse amplitudes and decay time constants, neither of which is used to define the QNG thresholds or the ideal-Fock comparison baselines.

free parameters (2)

Weight a in the robust QNG criterion Fn(a) = not fitted; scan parameter
The criterion uses a free weight a to combine Pn and Pn+1, producing a threshold curve. The experiment claims violation for some a, so a is a legitimate degree of freedom of the criterion rather than a parameter fit to the data.
Phonon-number decay time constants tau_n = tau_1 = 85(4) microseconds; tau_n = tau_1/n
Fitted to the exponential decay of Pn in Fig. 2(b) and used for the QNG-depth loss tolerance estimates and as a consistency check with the independently measured T1. These values do not set the QNG thresholds or the main fidelity claims.

assumptions (4)

domain assumption The cQAD system is described by the Jaynes-Cummings-type Hamiltonian in Eq. (1) with a qubit, a phonon mode, and a microwave drive.
Used to derive the optimal-control pulses and the RPN measurement basis functions; if additional modes or nonlinearities beyond this Hamiltonian are relevant, the state preparation and reconstruction could be biased.
domain assumption Energy relaxation and dephasing are modeled by a Lindblad master equation with collapse operators sqrt(kappa)a and sqrt(2 gamma_phi)a†a, as stated in Supplement II.
The predicted fidelities, the loss-adjusted Fisher information, and the RPN basis functions all rely on this decoherence model.
standard math The genuine n-phonon QNG definition in Eqs. (2)-(3) and the threshold Fn(a) computed from it are valid.
The QNG conclusion is obtained by comparing measured probabilities to this theoretical threshold; this is an established definition of the excluded state class.
domain assumption The RPN measurement reconstructs the phonon number distribution by fitting qubit population oscillations with simulated basis functions.
All Pn values used for QNG and Fisher information come from this fit; systematic errors in the basis functions would propagate into the main claims.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Genuine quantum non-Gaussianity and metrological sensitivity of Fock states prepared in a mechanical resonator." pith.science (2026). https://pith.science/paper/VFLNXNHP

@misc{pith2026241220971,
  author       = {Pith},
  title        = {Pith review of: Genuine quantum non-Gaussianity and metrological sensitivity of Fock states prepared in a mechanical resonator},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VFLNXNHP}},
  note         = {Machine review of arXiv:2412.20971}
}

abstract

Fock states of the quantum harmonic oscillator are fundamental to quantum sensing and information processing, serving as key resources for exploiting bosonic degrees of freedom. Here, we prepare high Fock states in a high-overtone bulk acoustic wave resonator (HBAR) by coupling it to a superconducting qubit and applying microwave pulses designed using quantum optimal control. We characterize the experimentally realized states by employing a criterion for genuine quantum non-Gaussianity (QNG) designed to reveal multiphonon contributions. Although energy relaxation and decoherence limit the achievable fidelities, we demonstrate genuine QNG features compatible with Fock state $\vert 6\rangle$, confirming that the prepared states cannot be generated through Gaussian operations on states with up to Fock state $\vert 5\rangle$ contributions. We further investigate the robustness of these QNG features to losses and their utility in sensing displacement amplitudes. In particular, we introduce a hierarchy based on the quantum Fisher information and show that, despite decoherence and measurement imperfections, the prepared states achieve a displacement sensitivity surpassing that of an ideal Fock state $\vert 3\rangle$. Our results have immediate applications in quantum sensing and simulations with HBAR devices.

Figures

Figures reproduced from arXiv: 2412.20971 by the authors.

**Figure 1.** (a) illustrates the fidelities of several Fock states prepared using optimal control pulses and measured with RPN. The blue points correspond to the fidelities obtained from the Schrodinger equation-based optimizer, which as- ¨ sumes a closed system and perfect state readout. To model decoherence during state preparation, we employ a master equation approach that includes the effects of decay and dephasing of both … view at source ↗

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

**Figure 8.** Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

**Figure 9.** Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p014_9.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

Quantum Phase Estimation Beyond the Gaussian Limit
quant-ph 2025-08 conditional novelty 5.0 of 10

Optimized asymmetric coherent-state superpositions can surpass the Gaussian bound for single-mode phase estimation, and the advantage persists under weak loss and noise up to a finite average-photon-number threshold.

Reference graph

Works this paper leans on

32 extracted references · 26 canonical work pages · cited by 1 Pith paper

[1]

Chamberland, K

C. Chamberland, K. Noh, P. Arrangoiz-Arriola, E. T. Campbell, C. T. Hann, J. Iverson, H. Putterman, T. C. Bohdanowicz, S. T. Flammia, A. Keller, et al., PRX Quantum 3, 010329 (2022)

work page 2022
[2]

H. Qiao, E. Dumur, G. Andersson, H. Yan, M.-H. Chou, J. Grebel, C. R. Conner, Y . J. Joshi, J. M. Miller, R. G. Povey, X. Wu, and A. N. Cleland, Science 380, 1030 (2023)

work page 2023
[3]

von L ¨upke, I

U. von L ¨upke, I. C. Rodrigues, Y . Yang, M. Fadel, and Y . Chu, Nature Physics 20, 564 (2024)

work page 2024
[4]

Marti, U

S. Marti, U. von L¨upke, O. Joshi, Y . Yang, M. Bild, A. Omahen, Y . Chu, and M. Fadel, Nature Physics 20, 1448 (2024)

work page 2024
[5]

C. T. Hann, C.-L. Zou, Y . Zhang, Y . Chu, R. J. Schoelkopf, S. M. Girvin, and L. Jiang, Phys. Rev. Lett. 123, 250501 (2019)

work page 2019
[6]

Schrinski, Y

B. Schrinski, Y . Yang, U. von L¨upke, M. Bild, Y . Chu, K. Horn- berger, S. Nimmrichter, and M. Fadel, Phys. Rev. Lett. 130, 133604 (2023)

work page 2023
[7]

M. Bild, M. Fadel, Y . Yang, U. von L¨upke, P. Martin, A. Bruno, and Y . Chu, Science380, 274 (2023)

work page 2023
[8]

Donadi and M

S. Donadi and M. Fadel, Phys. Rev. D 111, 026009 (2025)

work page 2025

Show all 32 references

[9]

Y . Chu, P. Kharel, T. Yoon, L. Frunzio, P. T. Rakich, and R. J. Schoelkopf, Nature 563, 666 (2018)

2018
[10]

von L ¨upke, Y

U. von L ¨upke, Y . Yang, M. Bild, L. Michaud, M. Fadel, and Y . Chu, Nature Physics18, 794 (2022)

2022
[11]

F. Wolf, C. Shi, J. C. Heip, M. Gessner, L. Pezz `e, A. Smerzi, M. Schulte, K. Hammerer, and P. O. Schmidt, Nat Commun 10, 2929 (2019)

2019
[12]

X. Deng, S. Li, Z.-J. Chen, Z. Ni, Y . Cai, J. Mai, L. Zhang, P. Zheng, H. Yu, C.-L. Zou, S. Liu, F. Yan, Y . Xu, and D. Yu, Nature Physics 20, 1874 (2024)

2024
[13]

Quantum metrology with a continuous-variable system,

M. Fadel, N. Roux, and M. Gessner, “Quantum metrology with a continuous-variable system,” (2024), arXiv:2411.04122 [quant-ph]

2024
[14]

C. Oh, K. Park, R. Filip, H. Jeong, and P. Marek, New Journal of Physics 22, 123039 (2020)

2020
[15]

G ´orecki, A

W. G ´orecki, A. Riccardi, and L. Maccone, Phys. Rev. Lett.129, 240503 (2022)

2022
[16]

Filip and L

R. Filip and L. Mi ˇsta, Phys. Rev. Lett. 106, 200401 (2011)

2011
[17]

Lachman, I

L. Lachman, I. Straka, J. Hlouˇsek, M. Jeˇzek, and R. Filip, Phys. Rev. Lett. 123, 043601 (2019)

2019
[18]

Podhora, L

L. Podhora, L. Lachman, T. Pham, A. Le ˇsund´ak, O. ˇC´ıp, L. Slodiˇcka, and R. Filip, Phys. Rev. Lett. 129, 013602 (2022)

2022
[19]

Khaneja, T

N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbr ¨uggen, and S. J. Glaser, Journal of magnetic resonance 172, 296 (2005)

2005
[20]

Eickbusch, V

A. Eickbusch, V . Sivak, A. Z. Ding, S. S. Elder, S. R. Jha, J. Venkatraman, B. Royer, S. M. Girvin, R. J. Schoelkopf, and M. H. Devoret, Nature Physics 18, 1464 (2022)

2022
[21]

Caneva, M

T. Caneva, M. Murphy, T. Calarco, R. Fazio, S. Montangero, V . Giovannetti, and G. E. Santoro, Phys. Rev. Lett.103, 240501 (2009)

2009
[22]

Hofheinz, E

M. Hofheinz, E. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. O’connell, H. Wang, J. M. Martinis, and A. Cle- land, Nature 454, 310 (2008)

2008
[23]

See supplementary materials
[24]

Chabaud, G

U. Chabaud, G. Roeland, M. Walschaers, F. Grosshans, V . Pa- rigi, D. Markham, and N. Treps, PRX Quantum 2, 020333 (2021)

2021
[25]

Fiur ´aˇsek, Opt

J. Fiur ´aˇsek, Opt. Express 30, 30630 (2022)

2022
[26]

Provazn´ık, L

J. Provazn´ık, L. Lachman, R. Filip, and P. Marek, Opt. Express 28, 14839 (2020). 6

2020
[27]

C. T. Lee, Phys. Rev. A 44, R2775 (1991)

1991
[28]

C. T. Lee, Phys. Rev. A 45, 6586 (1992)

1992
[29]

Straka, A

I. Straka, A. Predojevi ´c, T. Huber, L. Lachman, L. Butschek, M. Mikov´a, M. Mi ˇcuda, G. S. Solomon, G. Weihs, M. Je ˇzek, and R. Filip, Phys. Rev. Lett. 113, 223603 (2014)

2014
[30]

H. Kwon, K. C. Tan, T. V olkoff, and H. Jeong, Phys. Rev. Lett. 122, 040503 (2019)

2019
[31]

T. J. Sturges, T. McDermott, A. Buraczewski, W. R. Clements, J. J. Renema, S. W. Nam, T. Gerrits, A. Lita, W. S. Kolthammer, A. Eckstein, I. A. Walmsley, and M. Stobi ´nska, npj Quantum Information 7, 91 (2021)

2021
[32]

GENUINE QUANTUM NON-GAUSSIANITY AND METROLOGICAL SENSITIVITY OF FOCK STA TES PREPARED IN A MECHANICAL RESONA TOR

A. Ritboon, L. Slodi ˇcka, and R. Filip, Quantum Science and Technology 7, 015023 (2022). 1 SUPPLEMENTAL MA TERIAL FOR “GENUINE QUANTUM NON-GAUSSIANITY AND METROLOGICAL SENSITIVITY OF FOCK STA TES PREPARED IN A MECHANICAL RESONA TOR” I. SENSITIVITY FOR UNITARY EVOLUTIONS The m...

2022

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Chamberland, K

C. Chamberland, K. Noh, P. Arrangoiz-Arriola, E. T. Campbell, C. T. Hann, J. Iverson, H. Putterman, T. C. Bohdanowicz, S. T. Flammia, A. Keller, et al., PRX Quantum 3, 010329 (2022)

work page 2022

[2] [2]

H. Qiao, E. Dumur, G. Andersson, H. Yan, M.-H. Chou, J. Grebel, C. R. Conner, Y . J. Joshi, J. M. Miller, R. G. Povey, X. Wu, and A. N. Cleland, Science 380, 1030 (2023)

work page 2023

[3] [3]

von L ¨upke, I

U. von L ¨upke, I. C. Rodrigues, Y . Yang, M. Fadel, and Y . Chu, Nature Physics 20, 564 (2024)

work page 2024

[4] [4]

Marti, U

S. Marti, U. von L¨upke, O. Joshi, Y . Yang, M. Bild, A. Omahen, Y . Chu, and M. Fadel, Nature Physics 20, 1448 (2024)

work page 2024

[5] [5]

C. T. Hann, C.-L. Zou, Y . Zhang, Y . Chu, R. J. Schoelkopf, S. M. Girvin, and L. Jiang, Phys. Rev. Lett. 123, 250501 (2019)

work page 2019

[6] [6]

Schrinski, Y

B. Schrinski, Y . Yang, U. von L¨upke, M. Bild, Y . Chu, K. Horn- berger, S. Nimmrichter, and M. Fadel, Phys. Rev. Lett. 130, 133604 (2023)

work page 2023

[7] [7]

M. Bild, M. Fadel, Y . Yang, U. von L¨upke, P. Martin, A. Bruno, and Y . Chu, Science380, 274 (2023)

work page 2023

[8] [8]

Donadi and M

S. Donadi and M. Fadel, Phys. Rev. D 111, 026009 (2025)

work page 2025