Pith. sign in

REVIEW 5 minor 65 references

Coupling symmetry decides where lost quantum sensitivity goes—and whether it ever returns.

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 07:14 UTC pith:C6UGQPSU

load-bearing objection A careful, mostly exact theory paper tracing where encoded QFI sits when a spin chain meets a bosonic bath — worth a serious referee, with one caveat about the title claim of permanent loss.

arxiv 2607.21501 v1 pith:C6UGQPSU submitted 2026-07-23 quant-ph cond-mat.quant-gas

Flow of local sensitivity in a spin chain coupled to a bosonic bath

Marcin P{\l}odzie\'n This is my paper
classification quant-ph cond-mat.quant-gas PACS 03.65.Ta03.67.-a
keywords quantum Fisher informationspin chainbosonic bathJaynes-Cummings couplingHolstein couplingcorrelation deficitmetrological transportnon-Markovian revival
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.

This paper asks where the quantum Fisher information—the fundamental precision limit for phase estimation—goes when a spin chain carrying an encoded phase is coupled to a bosonic bath, and whether it can come back. Treating the bath as a full quantum system rather than tracing it out, the author finds that the coupling symmetry dictates the destination. An excitation-swapping Jaynes–Cummings coupling passes the departed sensitivity into the bath marginal, so a bath-only measurement can recover the phase; a density-type Holstein coupling leaves the bath blind to first order and stores the lost sensitivity entirely in spin–bath correlations. Whether the sensitivity returns to the spins is then governed by the bath spectrum: common periods mean full revival, while dispersed frequencies dephase the departed share and, within the observation window, keep it from ever returning.

Core claim

The central discovery is a destination rule: the symmetry of the spin–bath coupling alone decides which party holds the departed quantum Fisher information. For Jaynes–Cummings coupling, which conserves total excitation number, the single-excitation flow is a pure two-way exchange—F_s(j,t)=|a_j(t)|^2, F_b(j,t)=|b_j(t)|^2, and the spin–bath block adds nothing beyond its parts, so the correlation deficit vanishes identically. For Holstein coupling, which conserves spin-excitation number, the bath marginal has no term linear in the encoded angle, so a bath-only measurement returns zero first-order information; the lost sensitivity resides in spin–bath correlations, quantified by the correlation

What carries the argument

The workhorse is the block decomposition of the quantum Fisher information into spin, bath, and correlation parts, with the correlation deficit ΔF_sb = F_sb − F_s − F_b as the primary local diagnostic. For a single excitation under Jaynes–Cummings coupling, the problem reduces to independent momentum-space two-level systems with Rabi frequency Ω_q = sqrt(δ_q^2 + 4λ^2), whose occupation amplitudes are exactly the QFI densities; the bath spectrum enters through the spread of Ω_q. For Holstein coupling, a coherent boson cloud dresses each spin excitation and suppresses spin coherence by the Franck–Condon factor e^{−⟨N_b⟩}, which fixes the size of the deficit. The conserved global QFI serves as

Load-bearing premise

The claim that departed sensitivity 'never returns' assumes observations stay inside the boundary-reflection time of a finite bath; only in the infinite-chain limit is the loss strict.

What would settle it

Measure the site-summed bath QFI for a single excitation under Holstein coupling at zero encoded angle: the paper predicts exactly zero first-order information at all times, so any nonzero first-order bath QFI would falsify the destination rule. Alternatively, run a finite chain past the boundary-reflection time and watch for the predicted revival of the spin QFI, which the paper itself concedes occurs at that time.

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

If this is right

  • For a single excitation under Jaynes–Cummings coupling, a measurement confined to the bath can recover the full phase information, since the bath QFI equals the swapped occupancy.
  • Under Holstein coupling, a bath-only readout returns nothing to first order; recovering the lost sensitivity requires a joint spin–bath measurement, with the deficit giving the recoverable share.
  • When coupled-system frequencies share a common period, departed sensitivity revives fully and periodically; when they disperse, it dephases across the bath modes and, inside the observation window, never returns.
  • Soft bath modes act as a permanent information sink: as a mode frequency approaches zero, the correlation deficit climbs toward its maximum and the sensitivity it absorbs does not come back.
  • A transported metrological register can arrive with high fidelity while having lost most of its usable precision, because the block QFI scales as the square of the surviving coherence, not its first power.
  • For a GHZ probe on a dispersive Holstein bath, the Heisenberg advantage shrinks with probe size and can fall below the shot-noise limit, with no revival at any examined time.

Where Pith is reading between the lines

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

  • Beyond the paper: for finite chains, 'never returns' is a windowed statement—past the boundary-reflection time the departed share would reappear; strict non-return belongs to the infinite-chain limit, so an experiment on a finite device should see recurrences on long timescales.
  • Beyond the paper: metrological benchmarking of quantum channels should report Fisher information, not just transfer fidelity, since the fidelity–precision gap shown here is a generic quadratic-versus-linear effect of coherence loss.
  • Beyond the paper: the Holstein first-order null is protected by parity at any temperature, but at finite nonzero probe angle the bath does register the magnitude of the rotation; a sensor could exploit this to build a coarse bath-based detector while remaining blind to the sign.
  • Beyond the paper: if the destination rule extends to other generators and couplings, one could deliberately engineer a coupling symmetry to route sensitivity into a bath port as a protected memory—but only if the bath spectrum is commensurate, otherwise the information is effectively lost.

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

0 major / 5 minor

Summary. The paper introduces a block-QFI bookkeeping decomposition for a spin chain coupled to a structured bosonic bath and asks where locally encoded phase sensitivity goes: into the bath marginal, into spin-bath correlations, or back to the spins. For a single excitation under Jaynes-Cummings coupling, the authors prove F_s(j,t)=|a_j(t)|^2, F_b(j,t)=|b_j(t)|^2, and vanishing block deficit, so the flow is a reversible two-way exchange. For Holstein coupling they prove F_b=0 at the tangent level by parity, so the lost sensitivity is carried by spin-bath correlations. They then show that the bath spectrum controls revival: commensurate frequencies return the sensitivity, dispersed frequencies dephase it. The analysis is extended to GHZ probes and to transport on engineered perfect-state-transfer chains, with closed forms for the frozen GHZ case and TEBD numerics certified in App. F. The paper is careful in distinguishing exact results from estimates, and the finite-window nature of the 'never returns' claim is stated in Sec. II and App. B.

Significance. The main conceptual contribution is a symmetry-based 'destination rule' — the form of the coupling operator decides whether a bath-only readout can recover the phase at first order — together with a spectral criterion for information return. If correct, this gives a useful diagnostic for quantum metrology beyond Lindbladian master equations. The manuscript has real strengths: the single-excitation Jaynes-Cummings sector is solved exactly (Eqs. 12 and B1-B12); the Holstein F_b=0 statement is an exact symmetry result (App. E); the frozen GHZ probe has an exact closed form for every n (Eq. 18 and App. D); and the tensor-network computations are accompanied by explicit convergence checks (Fig. 13). I also credit the authors for flagging their own limitations: App. A states precisely which steps in Eq. (16) are approximations, and Sec. II/App. B qualify the finite-chain recurrence statement. These honest caveats make the paper more trustworthy, not less. The remaining issue is presentation-level: the abstract and conclusions state the permanent-loss claim without the caveat that the body correctly supplies.

minor comments (5)
  1. [Abstract; Sec. VI] The abstract's 'never returns' and the concluding 'permanent information sink' are unqualified, whereas the body is careful: Sec. II says that at finite L the decay is 'effective rather than strict' because the departed share returns on the boundary-reflection time, and App. B notes that for edge encoding the reflected amplitude returns immediately, giving a few-percent to ten-percent deviation from the infinite-chain result. Since 'never' is a thermodynamic-limit extrapolation, please add a clause such as 'in the thermodynamic limit, within the pre-recurrence window' to the abstract and conclusions.
  2. [Sec. III B, Eq. (16)] The relation F_s≈e^{-<N_b>} is presented as a coherent-cloud estimate, and App. A correctly lists the two approximation steps and the few-percent non-coherent correction. Consider adding a one-sentence pointer to App. A directly after Eq. (16) so that a reader who does not read the appendix does not mistake the estimate for an exact identity.
  3. [App. B, discussion after Eq. (B7)] The discussion of the mismatch between the open chain and the infinite-chain momentum forms is important, but it appears only in the appendix. A condensed version near Fig. 3 would help, because the plotted curves there are presented as exact open-chain solutions while Eq. (B7) is the infinite-chain reference; the current placement makes the distinction easy to miss.
  4. [Fig. 12 caption] The caption should state explicitly that the Holstein zeros at θ=0 and θ=π are first-order zeros at the tangent level, and that the bath QFI is nonzero for intermediate θ. The main text says this, but the figure alone could be misread as saying F_b vanishes for all angles at all times.
  5. [Data availability] The statement 'available from the author upon reasonable request' could be replaced by a repository or DOI, especially for the TEBD datasets behind Figs. 4-8. This is a reproducibility nicety rather than a substantive requirement.

Circularity Check

0 steps flagged

No significant circularity: central QFI-flow results are derived from the Hamiltonian and exact reduced-state formulas; approximations are labeled and checked.

full rationale

The paper's main derivations are self-contained rather than circular. The conserved total QFI is fixed by the initial generator and unitarity in App. A (F_global = 4 Var(G)), independent of the coupling and not fitted to the target quantities. The Jaynes–Cummings single-excitation relations F_s(j,t)=|a_j(t)|^2, F_b(j,t)=|b_j(t)|^2, and ΔF_sb=0 follow from the exact single-particle solution (App. B) together with the reduced-state QFI formula (Eq. A8), not from assuming the result; the same holds for the bath-side derivation in App. E. The Holstein destination rule F_b=0 at θ=0 is a symmetry consequence of the density coupling being even in θ, proven in Eqs. (E5)–(E7). The approximate coherent-cloud expression 1−e^{\langle N_b\rangle} is explicitly labeled an estimate (App. A: 'both are approximations', 'a good estimate over the range computed here') and is checked against TEBD numerics, not used as a fitting input. The finite-chain "never returns" statement is explicitly qualified in Sec. II as effective rather than strict, with recurrence on the boundary-reflection time, so it is a stated approximation rather than a hidden assumption. Self-citations appear for block-QFI tools (Refs. [21–24]), but the paper re-derives the needed formulas in App. A and does not use those citations to justify its central results. No fitted parameter is renamed as a prediction, no uniqueness claim is imported from the authors' prior work, and no equation reduces to its own input by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

The paper introduces no fitted parameters and no new physical entities. The 'correlation deficit' is a defined, measurable bookkeeping quantity, not an invented entity. The load-bearing premises are the closed-system zero-temperature setup, excitation-number conservation for the two couplings, the finite-window interpretation of permanent loss, and two acknowledged approximations used for estimates.

axioms (5)
  • domain assumption The joint system is closed, starts in the product state |⇑⟩|∅⟩, and evolves unitarily at zero temperature.
    This is the basis for the conserved total QFI and for excluding thermal noise; stated in Sec. II and App. A.
  • domain assumption The Holstein coupling conserves spin-excitation number; the Jaynes–Cummings coupling conserves total excitation number.
    Defines the solvable single-particle sector and underlies the destination rule; these are properties of the chosen standard Hamiltonians.
  • domain assumption The bath is a finite, structured reservoir; 'permanent loss' is interpreted before boundary-reflection time.
    Sec. II states that at finite L decay is effective rather than strict and that every window lies inside the reflection time; the 'never returns' claim depends on this windowing.
  • ad hoc to paper For Eq. (16), the bath state accompanying each excitation is approximated as a coherent cloud so the overlap is e^{-nbar}.
    Used to derive the estimate ¯F_s ≃ e^{-⟨N_b⟩}; the paper acknowledges this is an approximation, exact for the frozen independent-boson limit and deviating by a few percent for itinerant clouds.
  • domain assumption For Eq. (21), the arriving block density matrix is reduced to the two-dimensional sector spanned by |↓n⟩ and |↑n⟩.
    App. C states the reduction is exact only under spin-excitation-number conservation, which Holstein satisfies but Jaynes–Cummings does not.

pith-pipeline@v1.3.0-alltime-deepseek · 26253 in / 12624 out tokens · 124416 ms · 2026-08-01T07:14:20.155247+00:00 · methodology

0 comments
read the original abstract

We study how local sensitivity to an encoded parameter, captured by the quantum Fisher information, flows between a spin chain, a coupled bosonic bath, and their quantum correlations, where we treat the bath as a full many-body quantum system beyond the Lindbladian approximation. We analyze how the coupling symmetry determines the destination of the departed sensitivity directly at the level of the Hamiltonian. We consider an excitation-exchanging Jaynes--Cummings coupling, which preserves the total number of excitations, and a spin-excitation-conserving Holstein coupling. We find that the Holstein coupling leaves the bath with no first-order information about the phase and stores the lost sensitivity entirely in spin--bath correlations, whereas the Jaynes--Cummings coupling passes this sensitivity to the bath, in full for a single excitation. The bath spectrum then governs whether the sensitivity ever returns to the spins. It revives fully and periodically when the coupled-system frequencies share a common period, but when those frequencies disperse the departed share dephases across the bath modes and never returns. We note that a transported metrological register loses more sensitivity than its arrival fidelity implies.

Figures

Figures reproduced from arXiv: 2607.21501 by Marcin P{\l}odzie\'n.

Figure 1
Figure 1. Figure 1: FIG. 1. A schematic illustration of the physical model. A [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Jaynes–Cummings exchange at resonance on the uni [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Jaynes–Cummings off resonance [ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Holstein coupling on the uniform XX chain [ [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Correlation deficit of the itinerant Holstein coupling [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Scaling of the Heisenberg advantage with probe size [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. GHZ probe dynamics without transport [ [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Holstein GHZ block ( [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. QFI shares of an arriving GHZ block ( [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Space-time maps of the spin share [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Probe-angle dependence of the site-summed bath QFI [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Numerical certification of the tensor-network results. (a) Boson-cutoff convergence of the soft-mode sweep [Fig. [PITH_FULL_IMAGE:figures/full_fig_p020_13.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

65 extracted references · 2 linked inside Pith

  1. [1]

    Transfer of an entan- gled multi-qubit register on such a closed chain reaches fidelities above 0.99 for up to three qubits [58]

    narrives at the far end intact. Transfer of an entan- gled multi-qubit register on such a closed chain reaches fidelities above 0.99 for up to three qubits [58]. The pro- file makes the single-excitation block of the Hamiltonian the ˆJx operator of a spinj= (L−1)/2, so the single- particle propagator is a Wigner rotation matrix and the mirror time follows...

    2025

  2. [2]

    S. L. Braunstein and C. M. Caves, Phys. Rev. Lett.72, 3439 (1994)

    1994

  3. [3]

    M. G. A. Paris, Int. J. Quantum Inf.7, 125 (2009)

    2009

  4. [4]

    Pezz` e, A

    L. Pezz` e, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Rev. Mod. Phys.90, 035005 (2018)

    2018

  5. [5]

    T´ oth and I

    G. T´ oth and I. Apellaniz, J. Phys. A47, 424006 (2014)

    2014

  6. [6]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Science306, 1330 (2004)

    2004

  7. [7]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Nat. Photonics 5, 222 (2011)

    2011

  8. [8]

    B. M. Escher, R. L. de Matos Filho, and L. Davidovich, Nat. Phys.7, 406 (2011)

    2011

  9. [9]

    Demkowicz-Dobrza´ nski, J

    R. Demkowicz-Dobrza´ nski, J. Ko lody´ nski, and M. Gut ¸˘ a, Nat. Commun.3, 1063 (2012)

    2012

  10. [10]

    Smirne, J

    A. Smirne, J. Ko lody´ nski, S. F. Huelga, and R. Demkowicz-Dobrza´ nski, Phys. Rev. Lett.116, 120801 (2016)

    2016

  11. [11]

    Breuer and F

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

    2002

  12. [12]

    de Vega and D

    I. de Vega and D. Alonso, Rev. Mod. Phys.89, 015001 (2017)

    2017

  13. [13]

    Breuer, E.-M

    H.-P. Breuer, E.-M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)

    2009

  14. [14]

    Rivas, S

    ´A. Rivas, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett.105, 050403 (2010)

    2010

  15. [15]

    X.-M. Lu, X. Wang, and C. P. Sun, Phys. Rev. A82, 042103 (2010)

    2010

  16. [16]

    A. W. Chin, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett.109, 233601 (2012)

    2012

  17. [17]

    Rivas, S

    A. Rivas, S. F. Huelga, and M. B. Plenio, Rep. Prog. Phys.77, 094001 (2014)

    2014

  18. [18]

    Breuer, E.-M

    H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, Rev. 12 Mod. Phys.88, 021002 (2016)

    2016

  19. [19]

    Wysocki and J

    P. Wysocki and J. Chwede´ nczuk, Phys. Rev. Lett.134, 020201 (2025)

    2025

  20. [20]

    Wysocki, M

    P. Wysocki, M. P lodzie´ n, and J. Chwede´ nczuk, Phys. Rev. A112, 052443 (2025)

    2025

  21. [21]

    P lodzie´ n and J

    M. P lodzie´ n and J. Chwede´ nczuk, arXiv:2605.02774 (2026)

    Pith/arXiv arXiv 2026

  22. [22]

    P lodzie´ n and J

    M. P lodzie´ n and J. Chwede´ nczuk, Phys. Rev. Lett.136, 100204 (2026)

    2026

  23. [23]

    Wysocki, J

    P. Wysocki, J. Chwede´ nczuk, and M. P lodzie´ n, Phys. Rev. Lett.137, 030801 (2026)

    2026

  24. [24]

    P lodzie´ n and J

    M. P lodzie´ n and J. Chwede´ nczuk, Phys. Rev. A113, 062220 (2026)

    2026

  25. [25]

    P lodzie´ n and J

    M. P lodzie´ n and J. Chwede´ nczuk, arXiv:2605.00770 (2026)

    Pith/arXiv arXiv 2026

  26. [26]

    Holstein, Ann

    T. Holstein, Ann. Phys. (N.Y.)8, 325 (1959)

    1959

  27. [27]

    E. T. Jaynes and F. W. Cummings, Proc. IEEE51, 89 (1963)

    1963

  28. [28]

    C. B. Duke and G. D. Mahan, Phys. Rev.139, A1965 (1965)

    1965

  29. [29]

    G. D. Mahan,Many-Particle Physics, 3rd ed. (Kluwer Academic/Plenum, New York, 2000)

    2000

  30. [30]

    G. M. Palma, K.-A. Suominen, and A. K. Ekert, Proc. R. Soc. Lond. A452, 567 (1996)

    1996

  31. [31]

    T´ oth and D

    G. T´ oth and D. Petz, Phys. Rev. A87, 032324 (2013)

    2013

  32. [32]

    Gessner, L

    M. Gessner, L. Pezz` e, and A. Smerzi, Phys. Rev. A94, 020101 (2016)

    2016

  33. [33]

    W. H. Zurek, Nature Physics5, 181 (2009)

    2009

  34. [34]

    F. G. S. L. Brand˜ ao, M. Piani, and P. Horodecki, Nature Communications6, 7908 (2015)

    2015

  35. [35]

    Fert´ e and X

    B. Fert´ e and X. Cao, Phys. Rev. Lett.132, 110201 (2024)

    2024

  36. [36]

    Hyllus, W

    P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezz´ e, and A. Smerzi, Phys. Rev. A85, 022321 (2012)

    2012

  37. [37]

    T´ oth, Phys

    G. T´ oth, Phys. Rev. A85, 022322 (2012)

    2012

  38. [38]

    Pezz´ e and A

    L. Pezz´ e and A. Smerzi, Phys. Rev. Lett.102, 100401 (2009)

    2009

  39. [39]

    Chru´ sci´ nski and S

    D. Chru´ sci´ nski and S. Maniscalco, Phys. Rev. Lett.112, 120404 (2014)

    2014

  40. [40]

    John and J

    S. John and J. Wang, Phys. Rev. Lett.64, 2418 (1990)

    1990

  41. [41]

    Gonz´ alez-Tudela and J

    A. Gonz´ alez-Tudela and J. I. Cirac, Phys. Rev. Lett.119, 143602 (2017)

    2017

  42. [42]

    Gonz´ alez-Tudela and J

    A. Gonz´ alez-Tudela and J. I. Cirac, Phys. Rev. A96, 043811 (2017)

    2017

  43. [43]

    ˇSafr´ anek, Phys

    D. ˇSafr´ anek, Phys. Rev. A95, 052320 (2017)

    2017

  44. [44]

    Seveso, F

    L. Seveso, F. Albarelli, M. G. Genoni, and M. G. A. Paris, J. Phys. A: Math. Theor.53, 02LT01 (2020)

    2020

  45. [45]

    A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys.59, 1 (1987)

    1987

  46. [46]

    W. G. Unruh, Phys. Rev. A51, 992 (1995)

    1995

  47. [47]

    S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Phys. Rev. Lett.79, 3865 (1997)

    1997

  48. [48]

    Fr¨ owis and W

    F. Fr¨ owis and W. D¨ ur, Phys. Rev. Lett.106, 110402 (2011)

    2011

  49. [49]

    T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, W. A. Coish, M. Harlander, W. H¨ ansel, M. Hen- nrich, and R. Blatt, Phys. Rev. Lett.106, 130506 (2011)

    2011

  50. [50]

    J. H. Reina, L. Quiroga, and N. F. Johnson, Phys. Rev. A65, 032326 (2002)

    2002

  51. [51]

    T. J. Proctor, P. A. Knott, and J. A. Dunningham, Phys. Rev. Lett.120, 080501 (2018)

    2018

  52. [52]

    Zhuang, Z

    Q. Zhuang, Z. Zhang, and J. H. Shapiro, Phys. Rev. A 97, 032329 (2018)

    2018

  53. [53]

    X. Guo, C. R. Breum, J. Borregaard, S. Izumi, M. V. Larsen, T. Gehring, M. Christandl, J. S. Neergaard- Nielsen, and U. L. Andersen, Nat. Phys.16, 281 (2020)

    2020

  54. [54]

    B. K. Malia, Y. Wu, J. Mart ´ ınez-Rinc´ on, and M. A. Ka- sevich, Nature612, 661 (2022)

    2022

  55. [55]

    Bose, Phys

    S. Bose, Phys. Rev. Lett.91, 207901 (2003)

    2003

  56. [56]

    Christandl, N

    M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Phys. Rev. Lett.92, 187902 (2004)

    2004

  57. [57]

    Albanese, M

    C. Albanese, M. Christandl, N. Datta, and A. Ekert, Phys. Rev. Lett.93, 230502 (2004)

    2004

  58. [58]

    Kay, Int

    A. Kay, Int. J. Quantum Inf.8, 641 (2010)

    2010

  59. [59]

    Michel, M

    O. Michel, M. Werner, and A. Riera, Quantum Sci. Tech- nol.11, 035006 (2026)

    2026

  60. [60]

    Burgarth and S

    D. Burgarth and S. Bose, Phys. Rev. A73, 062321 (2006)

    2006

  61. [61]

    E. Baum, A. Broman, T. Clarke, N. C. Costa, J. Mucciac- cio, A. Yue, Y. Zhang, V. Norman, J. Patton, M. Radu- laski, and R. T. Scalettar, Phys. Rev. B105, 195429 (2022)

    2022

  62. [62]

    Apellaniz, M

    I. Apellaniz, M. Kleinmann, O. G¨ uhne, and G. T´ oth, Phys. Rev. A95, 032330 (2017). Appendix A: Reference state, block reduced states, and the block QFI Because ˆHis independent ofθ, the parameter derivative commutes with the evolution and the QFI atθ= 0 is fixed by the reference state and its tangent. Using−i ˆSy k | ↑⟩k = 1 2 | ↓⟩k, |Ψ0(t)⟩=e −i ˆHt |...

    2017

  63. [63]

    The 2Lproblem factorizes intoLindependent two-level systems, one perq, each pairing the bare spin-excitation energyε m q =−Jcosqwith the bare boson energyε b q =ω 0 −2t B cosq

    Reduction to two-level systems The swap acts on-site and conserves lattice momentumq= 2πm/L, so a spin excitation of momentumqcouples only to the boson of the same momentum. The 2Lproblem factorizes intoLindependent two-level systems, one perq, each pairing the bare spin-excitation energyε m q =−Jcosqwith the bare boson energyε b q =ω 0 −2t B cosq. Diagon...

  64. [64]

    The initial decay coefficient of the QFI is therefore bath-independent, fixed by the bare swap rate

    Limiting regimes (i) Short times.At times short compared with every 1/Ω q, the integrand expands as sin 2(Ωqt/2)/Ω2 q =t 2/4− Ω2 qt4/48 +O(t 6), and averaging with⟨Ω 2 q⟩= 4λ 2 +ω 2 0 + 1 2 (J−2t B)2 gives ¯F s(t) = 1−λ 2t2 + λ2 12 4λ2 +ω 2 0 + 1 2 (J−2t B)2 t4 +O(t 6).(B8) The leading term−λ 2t2 is set by the coupling alone, and the bath enters only at f...

  65. [65]

    Perfect-transfer Hamiltonian The engineered profile breaks translation invariance, so momentum no longer labels the modes of the chain of Sec. V. The profileJ i ∝ p i(L−i) makes the single-excitation block of the Hamiltonian the ˆJx operator of a spin j= (L−1)/2,H m =−s ˆJx withs= 2J/L, so the excitation spectrum is the equally spaced ladderε m m =−s m, m...