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REVIEW 3 major objections 5 minor 29 references

Many-Body Localization Induced by Correlated Disorder in Interacting Superconducting Qubits

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper argues that in strongly coupled transmon chains, the correlated disorder produced by external flux noise leaves the many-body localization transition essentially unchanged, with the critical dimensionless disorder strength…

desk verdict Useful hardware-to-disorder mapping, clean numerics, but the model actually simulated is under-specified and the robustness claim needs a direct uncorrelated control. read the letter →

arxiv 2608.07149 v1 pith:PPKQWWGK submitted 2026-08-07 quant-ph cond-mat.dis-nn

Thiago R. Girão Souza , Andreia Saguia , Alan C. Santos , Marcelo S. Sarandy This is my paper · ORCID
classification quant-phcond-mat.dis-nn
keywords many-bodylocalizationtransmonqubitscorrelateddisorderRényientropylocalmemoryparameterXYchainsuperconductingcircuits
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 asks whether many-body localization (MBL) survives in superconducting transmon arrays when disorder is correlated, as it inevitably is when random local fluxes shift both qubit frequencies and qubit-qubit couplings at once. It answers yes: by tuning junction asymmetry and reference flux, the correlations can be amplified, yet both the block-entanglement variance and a new local-memory parameter locate the MBL transition at roughly the same dimensionless disorder strength as the uncorrelated case. The paper also introduces a dynamics-based memory observable that requires only single-qubit population measurements, making the transition experimentally accessible without full state tomography. A sympathetic reading is that the transmon platform's intrinsic disorder correlations do not spoil its ability to host a localized phase, which matters for processor design.

What carries the argument

The argument runs through an effective spin-1/2 XY Hamiltonian whose on-site frequencies ω_m(φ) and couplings g_nm(φ) both inherit randomness from local fluxes φ_n. The dimensionless disorder parameter Δ(φ0)=δ(φ0)/J(φ0) maps hardware control (maximum flux φ0) onto the theory's disorder axis, and the covariance amplification coefficient A_m(φ0) quantifies how strongly coupling fluctuations track frequency fluctuations. Two diagnostics carry the numerical case: the disorder-ensemble variance of half-system Rényi-2 entropy, whose finite-size maximum marks the critical point, and a normalized local-memory parameter M(t) built from the profile distance D(t), whose late-time value crosses near Δ≈2 and whose derivative peaks sharpen with L.

What would settle it

A tractable calculation would be to simulate the transmon-derived XY Hamiltonian with the correlated off-diagonal fluctuations artificially amplified by a factor of ten so that they become comparable to the frequency disorder; if the variance peak of the half-system Rényi-2 entropy shifts noticeably from Δ≈2.17 or the memory-parameter crossing moves, the central robustness claim is falsified. Alternatively, an experiment on a transmon chain with CC/CS ≈ 0.2 measuring the entropy-variance peak location as a function of applied flux would settle the question directly.

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Extended reading notes

Core claim

The central claim is that correlated disorder in a transmon array leaves the MBL transition in close correspondence with the uncorrelated case, indicating that the transmon platform is robust against correlations in its random couplings and fields. This is established by exact diagonalization of an effective spin-1/2 XY chain derived from the transmon circuit: the disorder-ensemble variance of half-system Rényi-2 entropy peaks at a dimensionless disorder strength of about 2.17 for the largest size studied (L=14), and a newly introduced local-memory parameter, computed from the long-time dynamics of site occupations, shows a scale-invariant crossing near Δ≈2 with a derivative peak that sharpens with system size. The paper further shows that engineering the junction asymmetry and reference flux controls the covariance between frequency and coupling fluctuations, providing a hardware-level dial for correlated disorder.

Load-bearing premise

The entire comparison to the uncorrelated benchmark assumes that flux-induced fluctuations in the qubit-qubit couplings are substantially smaller than the frequency fluctuations, so that the dimensionless disorder Δ=δ(φ0)/J(φ0) is a faithful single-parameter description; the supplemental states this but provides no quantitative bound.

Editorial extensions

If this is right

  • A transmon chain with strong capacitive coupling (CC/CS ≈ 0.2) can be operated in a localized phase whose transition point is set by the same dimensionless disorder Δ≈2 seen in uncorrelated models, so existing MBL design rules transfer to realistic devices.
  • The local-memory parameter M(t) gives an experimentally cheap probe of MBL: only site occupations are needed, not entanglement tomography, and its crossing point agrees with entropy-based criticality.
  • Flux control can engineer correlated disorder patterns in situ; by choosing junction asymmetry α and reference flux φ0 the covariance amplification coefficient A_m(φ0) can be made large or small.
  • Mid-spectrum eigenstates show an area-law-to-volume-law crossover via the Rényi-2 entropy variance, with the variance maximum growing with system size, so finite devices up to L=14 already show the precursor of the MBL transition.

Reading between the lines

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

  • If the same robustness holds for next-nearest-neighbor and network-mediated couplings beyond the linear chain studied here, then MBL in two-dimensional transmon lattices would inherit the same insensitivity to correlated noise; the paper's mapping of flux-controlled disorder to an effective XY model gives a route to test this numerically.
  • The claim suggests a practical design principle: rather than engineering away correlated disorder, processors can tune junction asymmetry to operate at a flux sweet spot where correlations are weak enough that localization physics is unchanged.
  • A sharper test would be to measure the frequency-coupling covariance directly via two-qubit spectroscopy across many flux realizations; if Cov(ω_m, g_nm) scales as the paper's linearized expression, the effective model's premise is confirmed.
  • The finite-size critical estimates (Δ≈2.17 from entropy variance, Δ≈1.82 from memory derivative) leave a gap that presumably closes with L; extrapolating both to the thermodynamic limit would test whether correlated and uncorrelated transitions truly coincide.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper studies the MBL transition in linear transmon arrays whose qubit frequencies and couplings both depend on local external fluxes. The authors derive a covariance between on-site frequency fluctuations and coupling fluctuations (Eq. 2), show that this covariance can be amplified by choosing the junction asymmetry and reference flux (Fig. 1), and then use exact diagonalization for L=8-14 and time evolution for L=8-16 to extract critical disorder strengths from the variance of the half-system 2nd-order Rényi entropy and from a newly introduced local memory parameter. Their central conclusion is that correlated disorder, which is unavoidable in flux-tunable transmon devices, leaves the MBL transition in close correspondence with the uncorrelated case, with a critical dimensionless disorder near Δ≈2.

Significance. If substantiated, the robustness claim is practically important: it would mean that flux-tunable transmon arrays can be treated with standard diagonal-disorder MBL predictions even though the same flux fluctuations also modulate the couplings. The paper is also useful in proposing experimentally accessible probes (Rényi entropy via randomized measurements and single-site populations for the memory parameter), and in providing a reproducible GitHub repository for the processed data. The physical derivation of the covariance is straightforward, and the numerics are standard for finite-size MBL studies. However, the central claim requires the simulations to actually include the correlated couplings and to be compared with a same-model uncorrelated control; the manuscript as written does not establish either condition.

major comments (3)
  1. [Supplemental Material, Eq. (S2)] The effective disordered Hamiltonian in SM Eq. (S2) is written with generic hoppings J_nm and on-site terms h_m ∈ [-ΔJ, ΔJ], but the paper never states whether the J_nm used in Figs. 2 and 3 are drawn from the flux-dependent physical couplings g_nm(φ_n,φ_m) of Eq. (S4) or are fixed at their mean values. If the couplings are fixed, the simulated model is just the standard XY chain with independent diagonal disorder and the correlated-disorder claim is never tested; if they are sampled, the coupling-fluctuation amplitudes, the reference flux φ0, and the realization ensemble must be specified. The SM statement that 'weak correlated off-diagonal disorder' is 'naturally included' is not a substitute for reporting the actual distribution used in the numerics.
  2. [Conclusion and Entanglement signatures] The robustness claim is compared only to Ref. [17], an external frustrated XY chain, not to the uncorrelated version of the same transmon model. To conclude that 'correlated disorder leaves the MBL transition in close correspondence with the uncorrelated case,' the authors should simulate the same Hamiltonian with independent on-site disorder and fixed (or uncorrelated) couplings, and report the critical disorder estimates for both ensembles. Without this control, the agreement at Δ≈2 may reflect differences in the model or disorder distributions rather than robustness to correlations.
  3. [Quantum Dynamics, Fig. 3] The internal consistency of the two diagnostics is asserted rather than quantified: the derivative peak of the memory parameter at L=16 occurs at Δ*≈1.82, while the Rényi variance peak for L=14 occurs at (Δφ)_max≈2.17 and the von Neumann result is ≈2.41 (SM Fig. S2b). The manuscript calls these 'fully consistent' without finite-size extrapolations, error bars, or a scaling collapse. Since the central quantitative claim is that the correlated transition occurs at essentially the same disorder strength as the uncorrelated one, the spread of roughly 20-30% among the extracted points needs to be addressed.
minor comments (5)
  1. [Main text and SM, Eq. (S12)] The main text uses Δφ both for the random flux fluctuation and for the dimensionless disorder parameter Δ(φ0)=δ(φ0)/J(φ0) defined in SM Eq. (S12); the notation should be distinguished in Figs. 2-3 and throughout.
  2. [Title] The title says 'MBL Induced by Correlated Disorder', while the conclusion claims robustness of MBL against correlations; the title may overstate or mislead about what is demonstrated.
  3. [Fig. 1 caption] In Figs. 1(b,c), define ω1 and g12 explicitly, and state whether the plotted quantities are dimensionless and what flux distribution is used for the 3,000 realizations.
  4. [Eq. (1) and Fig. 1(a)] The Hamiltonian in Eq. (1) includes sums over all pairs m<n, but Fig. 1(a) depicts a linear chain; clarify which couplings are retained in the simulations and how the network-mediated non-local terms enter the numerical model.
  5. [Data Availability] The Github repository is a helpful resource; consider archiving the exact version of the scripts in a permanent repository, given that full production runs require HPC resources and are not included.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the MBL robustness claim is a numerical observation compared with an external benchmark, not an identity or a fitted result.

full rationale

The paper's derivation chain is: (i) a circuit-QED Hamiltonian (Eq. 1) with flux-dependent frequencies and couplings; (ii) a first-order covariance identity (Eq. 2 and SM Eq. S16) that defines the correlated-disorder strength rather than targeting a transition; (iii) exact diagonalization and time evolution under the effective disordered Hamiltonian (SM Eq. S2), with the control parameter Delta(phi0)=delta(phi0)/J(phi0) obtained from hardware parameters; and (iv) extraction of critical points from Var(S2) maxima and from d<M>/dDelta peaks. No step fits a parameter to the claimed MBL transition: Delta is defined before the numerics, the critical points are read from simulation data, and the reference value Delta~2 is taken from the external frustrated-XY study in Ref. [17]. Refs. [20] and [21], which include a coauthor, supply the mediated-coupling form entering Eq. (1), but that ingredient does not encode the robustness result and is independently grounded in circuit-QED derivations. The 'local memory parameter' in Eq. (5) is an imbalance-like diagnostic; using it to locate the transition is not a renaming that manufactures the result. The skeptic concern that the SM does not fully specify whether the couplings J_nm in the main runs are sampled from g_nm(phi_n,phi_m) is a reporting/validation gap, not a circular reduction: no quoted equation makes the predicted critical point equal to an input, and no fitted parameter is renamed as a prediction. The absence of a same-model uncorrelated control weakens the comparison but does not make the central conclusion an identity. The only mild circularity-adjacent feature is the use of self-cited mediated-coupling results in the modelling preamble, which is not load-bearing for the MBL robustness claim.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on standard circuit-QED expressions, a two-level transmon approximation, and standard MBL diagnostics from the literature. No new physical entities are introduced. The hand-chosen parameters that matter for the claim are the strong capacitive coupling ratio, the memory evaluation time, and the junction asymmetry parameter whose precise value is not stated for the main runs.

free parameters (3)
  • Capacitive participation ratio C_C/C_S = 0.2
    Chosen by hand to reach the strong-coupling regime ('Entering this regime is of pivotal relevance to our work because of the emergence of non-negligible non-local interacting terms', Sec. 2). The model and the correlated disorder effect depend on this choice.
  • Memory parameter evaluation time τ_L = ≈864 (t≈320 ns)
    Selected as the 'long evolution time' for computing ⟨M⟩ and its derivative (Fig. 3); no convergence test is provided, and the extracted critical point depends on this time.
  • Junction asymmetry parameter α = not specified explicitly for the MBL simulations (values up to 1.0 in Fig. 1)
    Controls the tunability range and the strength of the correlated disorder engineering (Sec. 2, Fig. 1); the value used for the exact diagonalization and time-evolution runs is not stated explicitly in the main text, which hinders reproducibility.
assumptions (6)
  • domain assumption Two-level approximation for each transmon qubit
    Invoked in Sec. 2 before Eq. (1): 'For highly anharmonic transmon artificial atoms, the two-level system approximation can be efficiently implemented for each transmon'. The effective spin model depends on this truncation.
  • domain assumption Josephson energy model for asymmetric loops, E_J(φ)=E_J0 sqrt(cos^2(πφ)+α^2 sin^2(πφ))
    Used to compute ω_m(φ) and g_nm(φ) in Sec. 2 and Supplemental Eqs. (S3)-(S4); this form sets the flux sensitivity that generates correlated disorder.
  • domain assumption Statistical independence of flux fluctuations, ⟨δφ_m δφ_n⟩=0
    Used in Eq. (2) and Supplemental Eq. (S15) to isolate the covariance; reasonable for separate flux lines but not empirically demonstrated here.
  • domain assumption Coupling fluctuations are much smaller than frequency fluctuations under applied flux
    Supplemental Material after Eq. (S12): 'these variations remain substantially smaller than the corresponding changes in the qubit frequencies'. This justifies mapping to a mainly on-site disorder model and defines Δ(φ0).
  • domain assumption Variance of block entanglement over disorder realizations peaks at the MBL critical point
    Adopted from Ref. [12] and used in Sec. 3 to extract (Δφ)max; a finite-size precursor rather than a direct thermodynamic-limit critical point.
  • domain assumption Uniform random distribution of local fluxes φ_n in [0, φ0] for each disorder realization
    Stated for Fig. S1 (500 realizations, each φ_n randomly in [0,0.5]) and used for the disorder ensemble; determines the relation between φ0 and Δ.

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Cite this review

Pith. "Pith review of Many-Body Localization Induced by Correlated Disorder in Interacting Superconducting Qubits." pith.science (2026). https://pith.science/paper/PPKQWWGK

@misc{pith2026260807149,
  author       = {Pith},
  title        = {Pith review of: Many-Body Localization Induced by Correlated Disorder in Interacting Superconducting Qubits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PPKQWWGK}},
  note         = {Machine review of arXiv:2608.07149}
}
read the original abstract

The failure of quantum thermalization due to Many-Body Localization (MBL) has evolved from a theoretical concept in spin chains to an experimental reality in synthetic quantum platforms, most notably superconducting circuits based on transmon qubits. Despite its significance, the MBL transition has been studied primarily under purely random disorder and local couplings, leaving more complex and realistic configurations largely unexplored. Here, we investigate the quantum dynamics of transmon networks subject to the unavoidable competing effects of correlated disorder and network-mediated non-local interactions. First, we show how to engineer the physical parameters of the quantum hardware to systematically control the correlated disorder patterns emerging in the system. Then, we demonstrate that the MBL phase transition is robust against such correlations, which is essential for tuning localization properties in realistic transmon devices. This robustness is established through the analysis of the block entanglement entropy variance across disorder realizations, which precisely locates the MBL critical point. Independently, we introduce a local memory parameter, whose dynamics at long evolution times reveals memory retention in the localized phase and yields a critical point consistent with the entropy analysis. These results provide a framework for understanding localization in complex quantum network topologies, with potential implications for multi-qubit processor design.

Figures

Figures reproduced from arXiv: 2608.07149 by the authors.

Figure 1
Figure 1. (a) Proposed experimental setup to observe MBL tran [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. (a) Mean half-system block entanglement ⟨S 2⟩, averaged over ten eigenstates in the middle of the spectrum, as a function of the disorder strength ∆ϕ for system sizes up to L = 14 spins. (b) Variance of the block entanglement over disorder ensembles as a function of ∆ϕ. The maximum grows with L and occurs at (∆ϕ)max ≈ 2.17 for L = 14. The parameters of the system are the same as in [PITH_FULL_IMAGE:figures/full_fig… view at source ↗
Figure 3
Figure 3. (a) Disorder-averaged late-time local-memory param [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Works this paper leans on

29 extracted references · 18 canonical work pages

  1. [17]

    M. S. Bahovadinov, D. V . Kurlov, S. I. Matveenko, B. L. Alt- shuler, and G. V . Shlyapnikov, Many-body localization transi- tion in a frustrated xy chain, Phys. Rev. B106, 075107 (2022)

    work page 2022

  2. [1]

    J. M. Deutsch, Quantum statistical mechanics in a closed sys- tem, Phys. Rev. A43, 2046 (1991)

    1991

  3. [2]

    Srednicki, Chaos and quantum thermalization, Phys

    M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994)

    1994

  4. [3]

    Rigol, V

    M. Rigol, V . Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature452, 854 (2008)

    2008

  5. [4]

    Nandkishore and D

    R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Annual Rev. Cond. Matt. Phys.6, 15 (2015)

    work page 2015

  6. [5]

    D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Collo- quium: Many-body localization, thermalization, and entangle- ment, Rev. Mod. Phys.91, 021001 (2019)

    2019

  7. [6]

    Sierant, M

    P. Sierant, M. Lewenstein, A. Scardicchio, L. Vidmar, and J. Za- krzewski, Many-body localization in the age of classical com- puting, Rep. Prog. Phys.88, 026502 (2025)

    work page 2025

  8. [7]

    Pawlik, M

    K. Pawlik, M. Prodius, P. R. Nic´acio Falc˜ao, and J. Zakrzewski, Facets of many body localization, arXiv:2601.09494 (2026)

    arXiv 2026

Show all 29 references
  1. [8]

    P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev.109, 1492 (1958)

    1958

  2. [9]

    I. V . Gornyi, A. D. Mirlin, and D. G. Polyakov, Interacting electrons in disordered wires: Anderson localization and low-t transport, Phys. Rev. Lett.95, 206603 (2005)

    2005

  3. [10]

    Basko, I

    D. Basko, I. Aleiner, and B. Altshuler, Metal–insulator transi- tion in a weakly interacting many-electron system with local- ized single-particle states, Annals of Physics321, 1126 (2006)

    2006

  4. [11]

    Pal and D

    A. Pal and D. A. Huse, Many-body localization phase transi- tion, Phys. Rev. B82, 174411 (2010)

    2010

  5. [12]

    J. A. Kj ¨all, J. H. Bardarson, and F. Pollmann, Many-body lo- calization in a disordered quantum ising chain, Phys. Rev. Lett. 113, 107204 (2014)

    2014

  6. [13]

    Schreiber, S

    M. Schreiber, S. S. Hodgman, P. Bordia, H. P. L ¨uschen, M. H. Fischer, R. V osk, E. Altman, U. Schneider, and I. Bloch, Ob- servation of many-body localization of interacting fermions in a quasirandom optical lattice, Science349, 842 (2015)

    2015

  7. [14]

    Smith, A

    J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, Many-body lo- calization in a quantum simulator with programmable random disorder, Nature Phys.12, 907 (2016)

    2016

  8. [15]

    Xu, J.-J

    K. Xu, J.-J. Chen, Y . Zeng, Y .-R. Zhang, C. Song, W. Liu, Q. Guo, P. Zhang, D. Xu, H. Deng, K. Huang, H. Wang, X. Zhu, D. Zheng, and H. Fan, Emulating many-body localization with a superconducting quantum processor, Phys. Rev. Lett.120, 050507 (2018)

    2018

  9. [16]

    Berke, E

    C. Berke, E. Varvelis, S. Trebst, A. Altland, and D. P. DiVin- cenzo, Transmon platform for quantum computing challenged by chaotic fluctuations, Nature Commun.13, 2495 (2022)

    2022

  10. [18]

    C.-K. Hu, G. Xie, K. Poulsen, Y . Zhou, J. Chu, C. Liu, R. Zhou, H. Yuan, Y . Shen, S. Liu, N. T. Zinner, D. Tan, A. C. Santos, 5 and D. Yu, Digital simulation of zero-temperature spontaneous symmetry breaking in a superconducting lattice processor, Na- ture Communications16, ...

    2025

  11. [19]

    Yanay, J

    Y . Yanay, J. Braum¨uller, T. P. Orlando, S. Gustavsson, C. Tahan, and W. D. Oliver, Mediated interactions beyond the nearest neighbor in an array of superconducting qubits, Phys. Rev. Appl.17, 034060 (2022)

    2022

  12. [20]

    Rosario, A

    P. Rosario, A. C. Santos, C. Villas-Boas, and R. Bachelard, Collateral coupling between superconducting resonators: Fast high-fidelity generation of qudit-qudit entanglement, Phys. Rev. Appl.20, 034036 (2023)

    2023

  13. [21]

    Caro Villanova and A

    C. Caro Villanova and A. C. Santos, Network-Mediated Ca- pacitive Coupling Drives Fast OTOC Saturation in Supercon- ducting Circuits, arXiv e-prints , arXiv:2605.05035 (2026), arXiv:2605.05035 [quant-ph]

    2026 arXiv

  14. [22]

    [12, 17, 23–25], for further details regard- ing strategies to engineer correlated disorder in the system and the V on-Neumann entropy analysis of the MBL transition

    See Supplemental Material appended to this manuscript, which also include the Refs. [12, 17, 23–25], for further details regard- ing strategies to engineer correlated disorder in the system and the V on-Neumann entropy analysis of the MBL transition

  15. [23]

    L. Ding, M. Hays, Y . Sung, B. Kannan, J. An, A. Di Paolo, A. H. Karamlou, T. M. Hazard, K. Azar, D. K. Kim, B. M. Niedzielski, A. Melville, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, J. A. Grover, K. Serniak, and W. D. Oliver, High-fidelity, frequency-flexible...

    2023

  16. [24]

    X. Wu, H. Yan, G. Andersson, A. Anferov, M.-H. Chou, C. R. Conner, J. Grebel, Y . J. Joshi, S. Li, J. M. Miller, R. G. Povey, H. Qiao, and A. N. Cleland, Modular quantum processor with an all-to-all reconfigurable router, Phys. Rev. X14, 041030 (2024)

    2024

  17. [25]

    J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schus- ter, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design derived from the cooper pair box, Phys. Rev. A76, 042319 (2007)

    2007

  18. [26]

    S. J. van Enk and C. W. J. Beenakker, Measuring Trρn on single copies ofρusing random measurements, Phys. Rev. Lett.108, 110503 (2012)

    2012

  19. [27]

    Elben, B

    A. Elben, B. Vermersch, M. Dalmonte, J. I. Cirac, and P. Zoller, R´enyi entropies from random quenches in atomic hubbard and spin models, Phys. Rev. Lett.120, 050406 (2018)

    2018

  20. [28]

    Brydges, A

    T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos, Probing r´enyi entan- glement entropy via randomized measurements, Science364, 260 (2019)

    2019

  21. [29]

    T. R. G. Souza, A. Saguia, A. C. Santos, and M. S. Sarandy, Transmon XY correlated disorder MBL: Re- producibility repository,https://github.com/thiagorgs/ transmon-xy-correlated-disorder-mbl(2026), GitHub repository. 6 Supplemental Material for: Many-Body Localization Induced...

    2026

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