Pith. sign in

REVIEW 2 major objections 5 minor 48 references

Prescriptive preparation and verification of nonstabilizer states

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Quantum state verification can steer state preparation, not just check it, cutting measurement cost by orders of magnitude.

desk verdict QSV-guided preparation is a real experimental step forward, but the trustworthiness of the headline fidelity number needs a correction or a caveat before it can be taken at face value. read the letter →

arxiv 2507.11180 v2 pith:MJSJ2WQE submitted 2025-07-15 quant-ph

Jian Li , Ye-Chao Liu , Xiao-Xiao Chen , Zhe Meng , Xing-Yan Fan , Wen-Hao Wang , Jie Ma , An-Ning Zhang
show 1 more author
Jiangwei Shang
This is my paper · ORCID
classification quant-ph
keywords quantumstateverificationnonstabilizerstatesWpreparationfidelityestimationhomogeneousQSVoperatortomographyentangledphotonpairs
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

Quantum state verification is usually a post-hoc pass/fail test applied only after a state has already been carefully prepared. This paper aims to turn QSV into the steering wheel of preparation itself: the same measurement operator that certifies a target state also provides a direct fidelity estimate, so experimental settings can be tuned against that estimate with no full tomography. Using nine measurement settings and $10^{4}$ samples on a three-qubit nonstabilizer W state, the authors report a QSV-estimated fidelity of 97.07(±0.26)%, while full tomography on roughly $10^{6}$ measurements reports 98.58(±0.12)%. The claim is that QSV is a resource-efficient, prescriptive alternative to tomography for real-time state engineering, not merely a diagnostic.

What carries the argument

The load-bearing object is the modified homogeneous QSV operator $\Omega_{\mathrm{Hom}}(W_3)$ of Eq. (5), a convex combination over permutations of a one-way adaptive measurement $\Omega^{\rightarrow}$. The adaptive measurement first projects all qubits except a preselected pair in the $Z$ basis; if no excitation is seen it tests the pair with $(XX)^+$, and if one excitation is seen it tests with $Z^+ Z^+$. Homogeneity means the same global operator is applied at every round, so the passing frequency can be inverted through the spectral gap $\nu = 1/2$ to give a direct fidelity estimate without reconstructing the state.

What would settle it

Compare the empirical passing frequency on states independently characterized by quantum state tomography and check whether $f = 1 - \nu(1 - F_{\mathrm{QST}})$ holds. With the reported numbers, the QSV estimate (97.07%) lies about 1.5 points below the QST value (98.58%), roughly 5 standard deviations, so a direct measurement of the realized operator's spectral gap under the actual wave-plate settings would settle whether the estimate is biased.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a modified homogeneous QSV operator can carry the full loop of preparation and verification. For the three-qubit W state, the operator $\Omega_{\mathrm{Hom}}(W_3) = \frac{1}{3}\sum_{k} P_k \Omega^{\rightarrow}$ built from one-way adaptive measurements has spectral gap $\nu = 1/2$, giving sample complexity $N = 2\epsilon^{-1}\ln\delta^{-1}$. Because the operator is homogeneous, the passing frequency $f$ directly estimates the average fidelity via $F = (f - (1-\nu))/\nu$. The experiment uses 9 measurement settings and $10^{4}$ samples to report 97.07(±0.26)% from QSV, independently matched by QST at 98.58(±0.12)% with 64 settings and about $10^{6}$ samples; a fitted scaling of $O(\epsilon^{-1.39})$ in the low-sample region is closer to QSV's Heisenberg-limited behavior than to tomography's $O(\epsilon^{-2})$.

Load-bearing premise

The entire quantitative claim rests on the assumption that the nine experimentally implemented measurement settings realize the ideal homogeneous verification operator with spectral gap exactly 1/2; if the realized operator deviates, the reported fidelity estimate is biased rather than merely noisy.

Editorial extensions

If this is right

  • With only a few dozen tests, the protocol can certify a fidelity lower bound; with thousands of tests, it estimates the average fidelity directly, and both modes avoid full state reconstruction.
  • The same 9 measurement settings and 10^4 samples produce a QSV fidelity of 97.07(±0.26)%, while QST uses 64 settings and roughly 10^6 samples to give 98.58(±0.12)%, so the method offers a drastic resource reduction for the same task.
  • The fitted scaling $O(\epsilon^{-1.39})$ in the low-sample regime outperforms the standard-quantum-limit scaling $O(\epsilon^{-2})$ of tomography, so the verification advantage is visible even before the asymptotic regime.
  • Because the QSV result guides tuning during preparation rather than only checking afterward, the protocol is a step toward real-time feedback control of quantum sources.

Reading between the lines

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

  • Editorial: if the unbiasedness assumption survives calibration, the same passing-frequency feedback loop could be attached to low-latency platforms to re-tune sources between operations, replacing QST in iterative alignment.
  • Editorial: the homogeneous-operator construction may transfer to other Dicke and nonstabilizer states whenever one can enforce a constant spectral gap, converting verification operators into online fidelity estimators for a broader class of targets.
  • Editorial: the 1.5-point gap between QSV and QST estimates, though within the paper's claim of consistency, suggests a useful stress test: repeated comparison under deliberately misaligned wave plates would map how sensitive the estimator is to spectral-gap mismatch.
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.

Referee Report

2 major / 5 minor

Summary. The manuscript reports an experimental implementation of a modified homogeneous quantum state verification (QSV) protocol for a three-qubit nonstabilizer W state, with the central claim that QSV can be used not only to certify but also to actively guide state preparation. Using nine measurement settings and 10^4 samples, the authors report a QSV-estimated fidelity of 97.07(±0.26)%, which they describe as consistent with a quantum state tomography (QST) fidelity of 98.58(±0.12)% obtained with roughly 10^6 measurements. The paper also presents two-qubit benchmarking, a scaling analysis of the required number of tests versus infidelity, and a comparison of QSV-guided and QST-guided preparation.

Significance. If the central claim is sound, the paper makes a useful conceptual advance: QSV is elevated from a post-hoc diagnostic to a prescriptive tool that can inform state preparation with far fewer resources than full tomography. The experimental demonstration is substantive, including an independent QST cross-check, a nonstabilizer target state, and a comparison of QSV-guided and QST-guided preparation in the two-qubit case. However, the quantitative agreement between the QSV fidelity estimate and the QST result is not statistically consistent, and the scaling exponent is presented without uncertainty. These issues directly affect the paper's main claims and require careful revision.

major comments (2)
  1. [Results, Eq. (10)] The reported QSV estimate of 97.07(±0.26)% and the QST value of 98.58(±0.12)% differ by 1.51 percentage points, which is about 5.3 combined standard deviations. This is not 'consistent' as claimed. More concretely, if the same ensemble had the QST fidelity 0.9858 and the implemented operator were exactly the ideal homogeneous operator of Eq. (5) with spectral gap ν = 1/2, the expected passing frequency would be f_exp = νF + (1-ν) = 0.9929. The observed frequency f = 0.98535 is about 6.3 binomial standard deviations below this value. The unbiasedness of the estimator in Eq. (10) is the load-bearing assumption behind the 'quantitative fidelity indicator' claim, so the discrepancy indicates either a deviation of the implemented POVM from Ω_Hom or a change of state between the QSV and QST runs. The manuscript must provide a systematic-error analysis, a same-ensemble comparison, or a revised claim that does not assert quantitative agreement.
  2. [Fig. 4(a) and scaling text] The claimed favorable scaling, stated as O(ε^-1.39), is obtained from a fit but no confidence interval, fit range, or goodness-of-fit is reported. The same is true for the two-qubit scaling exponents t = 1.45, 1.37, and 1.38 in Fig. S5. Since the claim of outperforming the standard quantum limit O(ε^-2) rests on this exponent, the authors should either provide a proper least-squares fit with parameter uncertainties and a defined fitting window, or explicitly label the exponent as an illustrative value obtained from a limited range rather than a quantitative result.
minor comments (5)
  1. [Eq. (7)] The hypothesis test uses n in the sums but N for the number of tests; the notation should be made consistent.
  2. [References] Several reference numbers are duplicated or inconsistent (for example, [2] is used for both Dicke and Pallister et al., and [3] for both Paris and Řeháček and Zhu and Hayashi), which makes it difficult to identify the cited works.
  3. [Summary] The sentence 'These features posits QSV' should be 'These features posit QSV'.
  4. [Fig. 4(a) caption] The legend entries 'verification' and 'estimation' are not fully explained; please clarify which symbols correspond to the certified upper bound and which to the direct estimate.
  5. [Introduction and Fig. 1] The term 'real-time' is used to describe the feedback loop, but the described procedure appears to involve manual adjustment of wave-plate angles guided by QSV results rather than automated closed-loop control; consider qualifying the wording to avoid overstating the degree of automation.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the fidelity estimate is a measured frequency converted by a standard inversion formula, and the QST result is an independent external benchmark.

full rationale

The paper's load-bearing derivation is not circular. Equation (10), F = (f - (1 - nu))/nu, is the standard inversion of the pass probability p = nu F + (1 - nu) for a homogeneous QSV operator; it is an unbiased estimator given the ideal operator, not a parameter fitted to the data and renamed as a prediction. The reported fidelity is a measured passing frequency converted through this known formula, and the QST result (98.58%) is an independent external benchmark rather than an input to the QSV estimate. The homogeneous protocol Ω_Hom in Eq. (5) and its sample complexity N = 2 epsilon^{-1} ln delta^{-1} are imported from the authors' prior work (Ref. [42]), and the original W-state protocol is imported from Ref. [20]; these are self-citations, but they are prior analytical results with stated assumptions, not assumptions whose conclusion is the present experimental claim. The numerical scaling O(epsilon^{-1.39}) is explicitly a fit to the experimental data, not a first-principles prediction that reduces to its own input. The observed gap between the QSV estimate (97.07%) and QST (98.58%) is a correctness/calibration concern about whether the implemented measurements match the ideal homogeneous operator, but it is not a circularity: no equation in the paper reduces to the claimed conclusion by construction.

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

The central quantitative claims rest on the QSV theoretical framework and the homogeneous protocol from prior literature rather than on new derivations. The only fitted quantities are descriptive scaling exponents from experimental data. No new entities are introduced.

free parameters (2)
  • scaling exponent t for W3 QSV = 1.39
    Exponent in the empirical scaling N ∝ ε^{-t} obtained by fitting experimental data in Fig. 4(a). This is a descriptive fit, not a prediction, and no confidence interval is given.
  • scaling exponents for two-qubit QSV runs = 1.45, 1.37, 1.38
    Fitted scaling exponents from Fig. S5 for the two-qubit states, used only to illustrate observed scaling behavior.
assumptions (4)
  • standard math QSV theoretical framework: sample complexity N ≈ (1/(ν ε)) ln(1/δ) for a verification operator with spectral gap ν.
    Adopted as the theoretical basis for verification bounds and estimation formulas, see Eqs. (1)-(10). This framework is established in the cited literature and is not re-derived here.
  • domain assumption The modified homogeneous QSV protocol for W3 (Eq. 5) has spectral gap ν = 1/2, so the sample complexity is 2 ε^{-1} ln δ^{-1}.
    Taken from Ref. 42 (Liu, Shang, Zhang et al., 2023), authored by three co-authors of this paper. The gap value is stated as a known result, not proven here.
  • domain assumption The source emits independent, identically distributed (i.i.d.) copies of the state in each round.
    QSV bounds and the Chernoff-Hoeffding significance statement (Eq. 9) assume i.i.d. rounds. The experiment does not test for drift or time correlations in the source.
  • standard math The homogeneous protocol allows unbiased direct fidelity estimation via Eq. (10).
    For a homogeneous operator Ω = |ψ><ψ| + (1-ν)(I - |ψ><ψ|), the passing frequency gives an unbiased estimate of fidelity. This is a standard property of homogeneous QSV protocols, stated in the text.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Prescriptive preparation and verification of nonstabilizer states." pith.science (2026). https://pith.science/paper/MJSJ2WQE

@misc{pith2026250711180,
  author       = {Pith},
  title        = {Pith review of: Prescriptive preparation and verification of nonstabilizer states},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MJSJ2WQE}},
  note         = {Machine review of arXiv:2507.11180}
}
abstract

High-fidelity quantum state preparation is a central task in quantum information science. In practice, it is commonly guided either by full quantum state tomography, which becomes prohibitively resource-intensive as system size grows, or by empirically chosen measurement settings that lack principled optimality. Here we show that quantum state verification (QSV) can be elevated from a purely diagnostic tool to a prescriptive framework for quantum state preparation, directly specifying experimentally optimal measurements and quantitative fidelity indicators without full state reconstruction. We experimentally realize this prescriptive paradigm using a three-qubit nonstabilizer $W$ state and a modified homogeneous QSV protocol. The verification measurements not only certify the prepared state with high confidence but also serve as a tomography-free indicator that systematically informs the preparation procedure. Using only nine measurement settings and $10^4$ samples, we achieve high-fidelity state preparation consistent with full tomography that requires orders of magnitude more resources. Beyond the present implementation, the prescriptive structure of QSV is naturally compatible with closed-loop feedback control, outlining a pathway toward genuine real-time quantum state preparation in future low-latency platforms.

Figures

Figures reproduced from arXiv: 2507.11180 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic illustration of real-time preparation and ver [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Verification protocol for an [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Experimental setup for the real-time preparation and verification of two-qubit states and three-qubit nonstabilizer [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Verified infidelity [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 44 canonical work pages

  1. [1]

    D. M. Greenberger, M. A. Horne, and A. Zeilinger, Bell’s theorem, quantum theory, and conceptions of the universe (Kluwer Academic, 1989) pp. 69–72

    work page 1989

  2. [2]

    R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954)

    1954

  3. [3]

    Paris and J

    M. Paris and J. ˇReh´aˇcek, eds., Quantum State Estimation , Lecture Notes in Physics, V ol. 649 (Springer-Verlag Berlin Heidelberg, 2004)

    work page 2004

  4. [4]

    T ´oth and O

    G. T ´oth and O. G¨uhne, Detecting genuine multipartite entan- glement with two local measurements, Phys. Rev. Lett. 94, 060501 (2005)

    work page 2005

  5. [5]

    S. T. Flammia and Y .-K. Liu, Direct fidelity estimation from few Pauli measurements, Phys. Rev. Lett. 106, 230501 (2011)

    work page 2011

  6. [6]

    Aolita, C

    L. Aolita, C. Gogolin, M. Kliesch, and J. Eisert, Reliable quantum certification of photonic state preparations, Nat. Commun. 6, 8498 (2015)

    work page 2015

  7. [7]

    Hayashi and T

    M. Hayashi and T. Morimae, Verifiable measurement-only blind quantum computing with stabilizer testing, Phys. Rev. Lett. 115, 220502 (2015)

    work page 2015

  8. [9]

    Zhang, Z

    W.-H. Zhang, Z. Li, G.-C. Li, X.-S. Hong, H. Zhu, G. Chen, C.-F. Li, and G.-C. Guo, Experimental verification of entan- gled states in the adversarial scenario, Phys. Rev. Appl. 23, 064005 (2025)

    work page 2025

Show all 48 references
  1. [10]

    Pallister, N

    S. Pallister, N. Linden, and A. Montanaro, Optimal verifica- tion of entangled states with local measurements, Phys. Rev. Lett. 120, 170502 (2018)

    2018

  2. [11]

    Morimae, Y

    T. Morimae, Y . Takeuchi, and M. Hayashi, Verification of hypergraph states, Phys. Rev. A 96, 062321 (2017)

    2017

  3. [12]

    Takeuchi and T

    Y . Takeuchi and T. Morimae, Verification of many-qubit states, Phys. Rev. X 8, 021060 (2018)

    2018

  4. [13]

    X.-D. Yu, J. Shang, and O. G ¨uhne, Optimal verification of general bipartite pure states, npj Quantum Inf. 5, 112 (2019)

    2019

  5. [14]

    Li, Y .-G

    Z. Li, Y .-G. Han, and H. Zhu, Efficient verification of bipar- tite pure states, Phys. Rev. A 100, 032316 (2019)

    2019

  6. [15]

    Wang and M

    K. Wang and M. Hayashi, Optimal verification of two-qubit pure states, Phys. Rev. A 100, 032315 (2019)

    2019

  7. [16]

    Zhu and M

    H. Zhu and M. Hayashi, Optimal verification and fidelity estimation of maximally entangled states, Phys. Rev. A 99, 052346 (2019)

    2019

  8. [17]

    Zhu and M

    H. Zhu and M. Hayashi, Efficient verification of hypergraph states, Phys. Rev. Appl. 12, 054047 (2019)

    2019

  9. [18]

    Zhu and M

    H. Zhu and M. Hayashi, E fficient verification of pure quan- tum states in the adversarial scenario, Phys. Rev. Lett. 123, 260504 (2019)

    2019

  10. [19]

    Zhu and M

    H. Zhu and M. Hayashi, General framework for verifying pure quantum states in the adversarial scenario, Phys. Rev. A 100, 062335 (2019)

    2019

  11. [20]

    Liu, X.-D

    Y .-C. Liu, X.-D. Yu, J. Shang, H. Zhu, and X. Zhang, Efficient verification of Dicke states, Phys. Rev. Appl. 12, 044020 (2019)

    2019

  12. [21]

    Li, Y .-G

    Z. Li, Y .-G. Han, and H. Zhu, Optimal verification of Greenberger-Horne-Zeilinger states, Phys. Rev. Appl. 13, 054002 (2020)

    2020

  13. [22]

    Dangniam, Y .-G

    N. Dangniam, Y .-G. Han, and H. Zhu, Optimal verification of stabilizer states, Phys. Rev. Research 2, 043323 (2020)

    2020

  14. [24]

    Jiang, K

    X. Jiang, K. Wang, K. Qian, Z. Chen, Z. Chen, L. Lu, L. Xia, F. Song, S. Zhu, and X. Ma, Towards the standard- ization of quantum state verification using optimal strategies, npj Quantum Inf. 6, 90 (2020)

    2020

  15. [25]

    Zhang, X

    W.-H. Zhang, X. Liu, P. Yin, X.-X. Peng, G.-C. Li, X.- Y . Xu, S. Yu, Z.-B. Hou, Y .-J. Han, J.-S. Xu, Z.-Q. Zhou, G. Chen, C.-F. Li, and G.-C. Guo, Classical communication enhanced quantum state verification, npj Quantum Inf.6, 103 (2020)

    2020

  16. [26]

    Li, Y .-G

    Z. Li, Y .-G. Han, H.-F. Sun, J. Shang, and H. Zhu, Veri- fication of phased Dicke states, Phys. Rev. A 103, 022601 (2021)

    2021

  17. [27]

    Y .-C. Liu, J. Shang, R. Han, and X. Zhang, Universally opti- mal verification of entangled states with nondemolition mea- surements, Phys. Rev. Lett. 126, 090504 (2021)

    2021

  18. [28]

    Y .-C. Liu, J. Shang, and X. Zhang, E fficient verification of entangled continuous-variable quantum states with local measurements, Phys. Rev. Research 3, L042004 (2021)

    2021

  19. [29]

    Y .-G. Han, Z. Li, Y . Wang, and H. Zhu, Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks, npj Quantum Inf.7, 164 (2021)

    2021

  20. [30]

    H. Zhu, Y . Li, and T. Chen, Efficient verification of ground states of frustration-free Hamiltonians, Quantum 8, 1221 (2024). 6

    2024

  21. [31]

    T. Chen, Y . Li, and H. Zhu, Efficient verification of Affleck- Kennedy-Lieb-Tasaki states, Phys. Rev. A 107, 022616 (2023)

    2023

  22. [32]

    Y . Li, H. Zhang, Z. Li, and H. Zhu, Minimum number of experimental settings required to verify bipartite pure states and unitaries, Phys. Rev. A 104, 062439 (2021)

    2021

  23. [33]

    X.-D. Yu, J. Shang, and O. G ¨uhne, Statistical methods for quantum state verification and fidelity estimation, Adv. Quantum Technol. 5, 2100126 (2022)

    2022

  24. [34]

    Zhang, C

    W.-H. Zhang, C. Zhang, Z. Chen, X.-X. Peng, X.-Y . Xu, P. Yin, S. Yu, X.-J. Ye, Y .-J. Han, J.-S. Xu, G. Chen, C.- F. Li, and G.-C. Guo, Experimental optimal verification of entangled states using local measurements, Phys. Rev. Lett. 125, 030506 (2020)

    2020

  25. [35]

    Jiang, K

    X. Jiang, K. Wang, K. Qian, Z. Chen, Z. Chen, L. Lu, L. Xia, F. Song, S. Zhu, and X. Ma, Towards the standard- ization of quantum state verification using optimal strategies, npj Quantum Inf 6, 90 (2020)

    2020

  26. [36]

    Zhang, X

    W.-H. Zhang, X. Liu, P. Yin, X.-X. Peng, G.-C. Li, X.-Y . Xu, S. Yu, Z.-B. Hou, Y .-J. Han, J.-S. Xu, et al. , Classi- cal communication enhanced quantum state verification, npj Quantum Inf 6, 103 (2020)

    2020

  27. [37]

    L. Xia, L. Lu, K. Wang, X. Jiang, S. Zhu, and X. Ma, Ex- perimental optimal verification of three-dimensional entan- glement on a silicon chip, New J. Phys. 24, 095002 (2022)

    2022

  28. [38]

    M. P. da Silva, O. Landon-Cardinal, and D. Poulin, Practi- cal characterization of quantum devices without tomography, Phys. Rev. Lett. 107, 210404 (2011)

    2011

  29. [39]

    Aaronson, Shadow tomography of quantum states, in Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018 (ACM, New York, NY , USA, 2018) p

    S. Aaronson, Shadow tomography of quantum states, in Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018 (ACM, New York, NY , USA, 2018) p. 325–338

    2018

  30. [40]

    Kliesch and I

    M. Kliesch and I. Roth, Theory of quantum system certifi- cation, PRX Quantum 2, 010201 (2021)

    2021

  31. [41]

    Leone, S

    L. Leone, S. F. E. Oliviero, and A. Hamma, Nonstabilizer- ness determining the hardness of direct fidelity estimation, Phys. Rev. A 107, 022429 (2023)

    2023

  32. [42]

    Y .-C. Liu, Y . Li, J. Shang, and X. Zhang, E fficient verifi- cation of arbitrary entangled states with homogeneous local measurements, Adv. Quantum Technol.6, 2300083 (2023)

    2023

  33. [43]

    Z. Meng, J. Yang, J. Li, X. Chen, Q. Wu, and A. Zhang, Ai polarization compensation algorithm using a asymmetry entangled photon source, Phys. Scr. 98, 125105 (2023)

    2023

  34. [44]

    J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Pro- posed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969)

    1969

  35. [45]

    See Supplemental Material for the Appendixes

  36. [46]

    Hoeffding, Probability inequalities for sums of bounded random variables, in The Collected Works of Wassily Hoeffd- ing (Springer, 1994) pp

    W. Hoeffding, Probability inequalities for sums of bounded random variables, in The Collected Works of Wassily Hoeffd- ing (Springer, 1994) pp. 409–426. 7 Supplemental Material: Real-time preparation and verification of nonstabilizer states Appendix A: Characterization of the ...

    1994

  37. [47]

    J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969)

    1969

  38. [48]

    Pallister, N

    S. Pallister, N. Linden, and A. Montanaro, Optimal verification of entangled states with local measurements, Phys. Rev. Lett. 120, 170502 (2018)

    2018

  39. [49]

    Zhu and M

    H. Zhu and M. Hayashi, General framework for verifying pure quantum states in the adversarial scenario, Phys. Rev. A100, 062335 (2019)

    2019

  40. [50]

    Shang, Z

    J. Shang, Z. Zhang, and H. K. Ng, Superfast maximum-likelihood reconstruction for quantum tomography, Phys. Rev. A95, 062336 (2017)

    2017

Pith tools

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