pith. sign in

arxiv: 2412.16062 · v1 · submitted 2024-12-20 · 🪐 quant-ph · cond-mat.stat-mech

Multipartite entanglement structure of monitored quantum circuits

Arnau Lira-Solanilla , Xhek Turkeshi , Silvia Pappalardi This is my paper

Pith reviewed 2026-05-23 06:21 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords monitored quantum circuitsmultipartite entanglementquantum Fisher informationmeasurement-induced phasesquantum criticalitysynthetic quantum matter
0
0 comments X

The pith

Unstructured monitored random circuits lack divergent multipartite entanglement even at criticality.

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

The paper uses quantum Fisher information to probe multipartite entanglement across phases of monitored quantum circuits. It establishes that random unstructured circuits show no divergence in this quantity at their critical points, marking a departure from the scaling seen in conventional quantum critical systems. The work further shows that two-site measurements can produce genuinely multipartite entangled phases when a protection mechanism is added. This perspective treats monitored circuits as synthetic matter whose phases are defined by their quantum information content.

Core claim

Unstructured monitored random circuits fail to exhibit divergent multipartite entanglement even at criticality, highlighting their departure from standard quantum critical behavior. However, genuinely multipartite entangled phases can be realized through two-site measurements, provided a protection mechanism is in place.

What carries the argument

Quantum Fisher information as a lens for multipartite entanglement structure in monitored phases.

If this is right

  • Multipartite entanglement serves as a diagnostic that distinguishes monitored phases from standard critical points.
  • Two-site measurements open a route to genuinely multipartite entangled phases when combined with protection.
  • The same perspective extends to the study of interacting monitored circuits and noisy quantum dynamics.
  • Unstructured random monitoring alone is insufficient to produce the entanglement scaling expected at criticality.

Where Pith is reading between the lines

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

  • Measurement-induced transitions in fully random circuits may belong to a distinct universality class that does not produce the usual entanglement divergences.
  • Protection mechanisms could be realized by adding symmetries or feedback rules that suppress local disentangling effects.
  • The approach invites comparison with other open-system settings where multipartite probes have been applied to phase transitions.

Load-bearing premise

A protection mechanism can be implemented to enable genuinely multipartite entangled phases via two-site measurements.

What would settle it

A direct computation of the quantum Fisher information in an unstructured monitored random circuit at the critical measurement rate that shows clear divergence would falsify the reported absence of divergent multipartite entanglement.

Figures

Figures reproduced from arXiv: 2412.16062 by Arnau Lira-Solanilla, Silvia Pappalardi, Xhek Turkeshi.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) Schematic description of a particular disorder real [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Average stationary state QFI for Haar (a) and sta [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: QFI as a function of the single-qubit measurement [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (main) Phase diagram characterizing the multipartite [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (main) Phase diagram of the TMI in the structured [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Phase diagram of the QFI in the circuit with random [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

Monitored quantum circuits have attracted significant interest as an example of synthetic quantum matter, intrinsically defined by their quantum information content. Here, we propose a multipartite entanglement perspective on monitored phases through the lens of quantum Fisher information. Our findings reveal that unstructured monitored random circuits fail to exhibit divergent multipartite entanglement even at criticality, highlighting their departure from standard quantum critical behavior. However, we demonstrate that genuinely multipartite entangled phases can be realized through two-site measurements, provided a protection mechanism is in place. This work positions multipartite entanglement as a valuable perspective for the study of interacting monitored circuits and broader frameworks of noisy quantum dynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes a multipartite entanglement perspective on monitored quantum phases via quantum Fisher information. It claims that unstructured monitored random circuits do not exhibit divergent multipartite entanglement even at criticality (departing from standard quantum critical behavior) but that genuinely multipartite entangled phases can be realized through two-site measurements when a protection mechanism is present.

Significance. If the claims are substantiated with explicit constructions and scaling data, the work would supply a new diagnostic for entanglement structure in monitored circuits and a route to engineering multipartite phases under noise, potentially broadening the classification of measurement-induced phases beyond bipartite measures.

major comments (1)
  1. [Abstract] Abstract: the central positive claim—that genuinely multipartite entangled phases are realized via two-site measurements 'provided a protection mechanism is in place'—is load-bearing yet supplies no definition, circuit modification, measurement protocol, or Fisher-information calculation, rendering the claim unevaluable from the given text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their comments. The primary concern raised is that the abstract's central claim lacks sufficient detail to be evaluable. We agree that the abstract is concise and will revise it to better summarize the key elements while pointing to the main text for definitions and calculations.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central positive claim—that genuinely multipartite entangled phases are realized via two-site measurements 'provided a protection mechanism is in place'—is load-bearing yet supplies no definition, circuit modification, measurement protocol, or Fisher-information calculation, rendering the claim unevaluable from the given text.

    Authors: We acknowledge that the abstract, standing alone, does not define the protection mechanism, specify the circuit modification, detail the measurement protocol, or include the Fisher-information calculation. The full manuscript develops these elements in the main text with explicit constructions. To make the claim more evaluable from the abstract itself, we will revise it to include a brief definition of the protection mechanism and reference the relevant sections containing the protocols and scaling data. revision: yes

Circularity Check

0 steps flagged

No circularity: abstract presents claims without any derivation chain or self-referential structure

full rationale

The provided document consists solely of the abstract, which states findings from a proposed perspective on monitored circuits using quantum Fisher information. No equations, derivations, fitted parameters, or citations appear. Claims about unstructured circuits and multipartite phases via two-site measurements are framed as empirical or analytical results rather than definitions or tautologies. No self-citation load-bearing steps, ansatzes, or renamings are present. The derivation chain cannot be walked because none is supplied; the text is self-contained as a high-level summary of external analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, derivations, or invented entities; the sole identifiable assumption is the suitability of quantum Fisher information as a multipartite-entanglement probe.

axioms (1)
  • domain assumption Quantum Fisher information serves as a valid lens for multipartite entanglement structure in monitored quantum circuits
    The entire perspective is proposed through this lens (abstract, second sentence).

pith-pipeline@v0.9.0 · 5603 in / 1227 out tokens · 62669 ms · 2026-05-23T06:21:07.593589+00:00 · methodology

discussion (0)

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

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Rise and fall of nonstabilizerness via random measurements

    quant-ph 2025-07 conditional novelty 7.0

    Analytical and numerical study of stabilizer nullity and Rényi entropies in monitored Clifford circuits shows quantized decay for computational measurements and size-dependent relaxation to a non-trivial steady state ...

Reference graph

Works this paper leans on

103 extracted references · 103 canonical work pages · cited by 1 Pith paper · 3 internal anchors

  1. [1]

    Preskill, Quantum 2, 79 (2018)

    J. Preskill, Quantum 2, 79 (2018)

    work page 2018

  2. [2]

    M. P. Fisher, V. Khemani, A. Nahum, and S. Vijay, Annu. Rev. Condens. Matter Phys. 14, 335 (2023)

    work page 2023

  3. [3]

    M. J. Gullans and D. A. Huse, Phys. Rev. X 10, 041020 (2020)

    work page 2020

  4. [4]

    M. J. Gullans, S. Krastanov, D. A. Huse, L. Jiang, and S. T. Flammia, Phys. Rev. X 11, 031066 (2021)

    work page 2021

  5. [5]

    Ippoliti and V

    M. Ippoliti and V. Khemani, PRX Quantum 5, 020304 (2024)

    work page 2024

  6. [6]

    Agrawal, J

    U. Agrawal, J. Lopez-Piqueres, R. Vasseur, S. Gopalakr- ishnan, and A. C. Potter, Phys. Rev. X 14, 041012 (2024)

    work page 2024

  7. [7]

    Turkeshi and P

    X. Turkeshi and P. Sierant, Phys. Rev. Lett. 132, 140401 (2024)

    work page 2024

  8. [8]

    Lovas, U

    I. Lovas, U. Agrawal, and S. Vijay, PRX Quantum 5, 030327 (2024)

    work page 2024

  9. [9]

    Fert´ e and X

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

    work page 2024

  10. [10]

    Amico, R

    L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008)

    work page 2008

  11. [11]

    Horodecki, P

    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    work page 2009

  12. [12]

    Calabrese and J

    P. Calabrese and J. Cardy, J. Phys. A: Math. Theor. 42, 504005 (2009)

    work page 2009

  13. [13]

    Laflorencie, Phys

    N. Laflorencie, Phys. Rep. 646, 1 (2016)

    work page 2016

  14. [14]

    C. Noel, P. Niroula, D. Zhu, A. Risinger, L. Egan, D. Biswas, M. Cetina, A. V. Gorshkov, M. J. Gullans, D. A. Huse, and C. Monroe, Nat. Phys. 18, 760 (2022)

    work page 2022

  15. [15]

    J. M. Koh, S.-N. Sun, M. Motta, and A. J. Minnich, Nat. Phys. 19, 1314 (2023)

    work page 2023

  16. [16]

    Google AI Quantum and collaborators, Nature 622, 481 (2023)

    work page 2023

  17. [17]

    A. C. Potter and R. Vasseur, Entanglement dynamics in hybrid quantum circuits, inEntanglement in Spin Chains (Springer International Publishing, 2022) p. 211

    work page 2022

  18. [18]

    O. Lunt, J. Richter, and A. Pal, Quantum simulation us- ing noisy unitary circuits and measurements, inEntangle- ment in Spin Chains (Springer International Publishing,

    work page

  19. [19]

    Y. Li, X. Chen, and M. P. Fisher, Phys. Rev. B 98, 205136 (2018)

    work page 2018

  20. [20]

    Y. Li, X. Chen, and M. P. Fisher, Phys. Rev. B 100, 134306 (2019)

    work page 2019

  21. [21]

    Skinner, J

    B. Skinner, J. Ruhman, and A. Nahum, Phys. Rev. X 9, 031009 (2019)

    work page 2019

  22. [22]

    Jian, Y.-Z

    C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Ludwig, 6 Phys. Rev. B 101, 104302 (2020)

    work page 2020

  23. [23]

    Y. Bao, S. Choi, and E. Altman, Phys. Rev. B 101, 104301 (2020)

    work page 2020

  24. [24]

    Chitambar and G

    E. Chitambar and G. Gour, Rev. Mod. Phys. 91, 025001 (2019)

    work page 2019

  25. [25]

    Sierant and X

    P. Sierant and X. Turkeshi, Phys. Rev. Lett. 128, 130605 (2022)

    work page 2022

  26. [26]

    S. P. Kelly, U. Poschinger, F. Schmidt-Kaler, M. P. A. Fisher, and J. Marino, SciPost Phys. 15, 250 (2023)

    work page 2023

  27. [27]

    Colmenarez, Z.-M

    L. Colmenarez, Z.-M. Huang, S. Diehl, and M. M¨ uller, Phys. Rev. Res. 6, L042014 (2024)

    work page 2024

  28. [28]

    Eckstein, B

    F. Eckstein, B. Han, S. Trebst, and G.-Y. Zhu, PRX Quantum 5, 040313 (2024)

    work page 2024

  29. [29]

    F. Venn, J. Behrends, and B. B´ eri, Phys. Rev. Lett.131, 060603 (2023)

    work page 2023

  30. [30]

    Niroula, C

    P. Niroula, C. D. White, Q. Wang, S. Johri, D. Zhu, C. Monroe, C. Noel, and M. J. Gullans, Nat. Phys. 20, 1786–1792 (2024)

    work page 2024

  31. [31]

    Bejan, C

    M. Bejan, C. McLauchlan, and B. B´ eri, PRX Quantum 5, 030332 (2024)

    work page 2024

  32. [32]

    G. E. Fux, E. Tirrito, M. Dalmonte, and R. Fazio, Phys. Rev. Res. 6, L042030 (2024)

    work page 2024

  33. [33]

    Paviglianiti, G

    A. Paviglianiti, G. Lami, M. Collura, and A. Silva, (2024), arXiv:2405.06054 [quant-ph]

    work page arXiv 2024

  34. [34]

    A. Gu, S. F. E. Oliviero, and L. Leone, (2024), arXiv:2403.19610 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  35. [35]

    Cheng, E

    Z. Cheng, E. Huang, V. Khemani, M. J. Gullans, and M. Ippoliti, (2024), arXiv:2412.04414 [quant-ph]

    work page arXiv 2024

  36. [36]

    M. J. Gullans and D. A. Huse, Phys. Rev. Lett. 125, 070606 (2020)

    work page 2020

  37. [37]

    Y. Li, Y. Zou, P. Glorioso, E. Altman, and M. P. A. Fisher, Phys. Rev. Lett. 130, 220404 (2023)

    work page 2023

  38. [38]

    Kamakari, J

    H. Kamakari, J. Sun, Y. Li, J. J. Thio, T. P. Gujarati, M. P. A. Fisher, M. Motta, and A. J. Minnich, (2024), arXiv:2403.00938 [quant-ph]

    work page arXiv 2024

  39. [39]

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

    work page 1994

  40. [40]

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

    work page 2009

  41. [41]

    Pezz´ e and A

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

    work page 2009

  42. [42]

    Giovannetti, S

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

    work page 2011

  43. [43]

    Hyllus, W

    P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezz´ e, and A. Smerzi, Phys. Rev. A 85, 022321 (2012)

    work page 2012

  44. [44]

    T´ oth, Phys

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

    work page 2012

  45. [45]

    T´ oth and I

    G. T´ oth and I. Apellaniz, J. Phys. A: Math. Theor. 47, 424006 (2014)

    work page 2014

  46. [46]

    Quantum theory of phase estimation

    L. Pezze’ and A. Smerzi, (2014), arXiv:1411.5164 [quant- ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  47. [47]

    Pezz` e, A

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

    work page 2018

  48. [48]

    J. Liu, H. Yuan, X.-M. Lu, and X. Wang, J. Phys. A: Math. Theor. 53, 023001 (2019)

    work page 2019

  49. [49]

    M. Yu, Y. Liu, P. Yang, M. Gong, Q. Cao, S. Zhang, H. Liu, M. Heyl, T. Ozawa, N. Goldman, and J. Cai, npj Quantum Info. 8, 56 (2022)

    work page 2022

  50. [50]

    Paviglianiti and A

    A. Paviglianiti and A. Silva, Phys. Rev. B 108, 184302 (2023)

    work page 2023

  51. [51]

    Passarelli, X

    G. Passarelli, X. Turkeshi, A. Russomanno, P. Lucig- nano, M. Schir` o, and R. Fazio, Phys. Rev. Lett. 132, 163401 (2024)

    work page 2024

  52. [52]

    P. M. Poggi and M. H. Mu˜ noz-Arias, Quantum 8, 1229 (2024)

    work page 2024

  53. [53]

    D. M. Greenberger, M. A. Horne, and A. Zeilinger, (2007), arXiv:0712.0921 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  54. [54]

    Throughout this work, the Pauli matrices acting on site i are denoted as ˆσα i with α = x, y, z

    work page

  55. [55]

    C. N. Yang, Rev. Mod. Phys. 34, 694 (1962)

    work page 1962

  56. [56]

    Hauke, M

    P. Hauke, M. Heyl, L. Tagliacozzo, and P. Zoller, Nat. Phys. 12, 778 (2016)

    work page 2016

  57. [57]

    Pezz` e, M

    L. Pezz` e, M. Gabbrielli, L. Lepori, and A. Smerzi, Phys. Rev. Lett. 119, 250401 (2017)

    work page 2017

  58. [58]

    Pappalardi, A

    S. Pappalardi, A. Russomanno, A. Silva, and R. Fazio, J. Stat. Mech.: Theory Exp. 2017 (5), 053104

    work page 2017

  59. [59]

    Brenes, S

    M. Brenes, S. Pappalardi, J. Goold, and A. Silva, Phys. Rev. Lett. 124, 040605 (2020)

    work page 2020

  60. [60]

    Laurell, A

    P. Laurell, A. Scheie, C. J. Mukherjee, M. M. Koza, M. Enderle, Z. Tylczynski, S. Okamoto, R. Coldea, D. A. Tennant, and G. Alvarez, Phys. Rev. Lett. 127, 037201 (2021)

    work page 2021

  61. [61]

    Scheie, P

    A. Scheie, P. Laurell, A. M. Samarakoon, B. Lake, S. E. Nagler, G. E. Granroth, S. Okamoto, G. Alvarez, and D. A. Tennant, Phys. Rev. B 103, 224434 (2021)

    work page 2021

  62. [62]

    Vitale, A

    V. Vitale, A. Rath, P. Jurcevic, A. Elben, C. Branciard, and B. Vermersch, PRX Quantum 5, 030338 (2024)

    work page 2024

  63. [63]

    Fr´ erot and T

    I. Fr´ erot and T. Roscilde, Phys. Rev. Lett. 121, 020402 (2018)

    work page 2018

  64. [64]

    M. M. Rams, P. Sierant, O. Dutta, P. Horodecki, and J. Zakrzewski, Phys. Rev. X 8, 021022 (2018)

    work page 2018

  65. [65]

    Y. Chu, S. Zhang, B. Yu, and J. Cai, Phys. Rev. Lett. 126, 010502 (2021)

    work page 2021

  66. [66]

    Zabalo, M

    A. Zabalo, M. J. Gullans, J. H. Wilson, S. Gopalakrish- nan, D. A. Huse, and J. H. Pixley, Phys. Rev. B 101, 060301 (2020)

    work page 2020

  67. [67]

    Zabalo, M

    A. Zabalo, M. J. Gullans, J. H. Wilson, R. Vasseur, A. W. W. Ludwig, S. Gopalakrishnan, D. A. Huse, and J. H. Pixley, Phys. Rev. Lett. 128, 050602 (2022)

    work page 2022

  68. [68]

    Sierant, M

    P. Sierant, M. Schir` o, M. Lewenstein, and X. Turkeshi, Phys. Rev. B 106, 214316 (2022)

    work page 2022

  69. [69]

    Y. Li, X. Chen, A. W. W. Ludwig, and M. P. A. Fisher, Phys. Rev. B 104, 104305 (2021)

    work page 2021

  70. [70]

    Desaules, F

    J.-Y. Desaules, F. Pietracaprina, Z. Papi´ c, J. Goold, and S. Pappalardi, Phys. Rev. Lett. 129, 020601 (2022)

    work page 2022

  71. [71]

    Specifi- cally, the local rotations depend on the evolution oper- ator U (nj ) j (U), and averaging over circuit realizations is non-linear, cf

    Crucially, the computation remains non-trivial even in the limit p → 0, corresponding to purely unitary dynam- ics |ψt⟩ = U |ψ0⟩ for some unitary operator U. Specifi- cally, the local rotations depend on the evolution oper- ator U (nj ) j (U), and averaging over circuit realizations is non-linear, cf. also Ref. [50]. A similar reasoning holds also in the ...

    work page

  72. [72]

    X. Chen, Y. Li, M. P. A. Fisher, and A. Lucas, Phys. Rev. Res. 2, 033017 (2020)

    work page 2020

  73. [73]

    Lang and H

    N. Lang and H. P. B¨ uchler, Phys. Rev. B 102, 094204 (2020)

    work page 2020

  74. [74]

    P. S. Tarabunga and E. Tirrito, (2024), arXiv:2407.15939 [quant-ph]

    work page arXiv 2024

  75. [75]

    Rep. Prog. Phys. 43, 833 (1980)

    work page 1980

  76. [76]

    S. Sang, Y. Li, T. Zhou, X. Chen, T. H. Hsieh, and M. P. Fisher, PRX Quantum 2, 030313 (2021)

    work page 2021

  77. [77]

    Nahum and B

    A. Nahum and B. Skinner, Phys. Rev. Res. 2, 023288 (2020)

    work page 2020

  78. [78]

    Klocke and M

    K. Klocke and M. Buchhold, Phys. Rev. B 106, 104307 (2022)

    work page 2022

  79. [79]

    Klocke and M

    K. Klocke and M. Buchhold, Phys. Rev. X 13, 041028 (2023)

    work page 2023

  80. [80]

    Merritt and L

    J. Merritt and L. Fidkowski, Phys. Rev. B 107, 064303 7 (2023)

    work page 2023

Showing first 80 references.