pith. sign in

arxiv: 2606.25061 · v1 · pith:2M4TTWQVnew · submitted 2026-06-23 · 🪐 quant-ph · cond-mat.mes-hall

Nonlocal Quantum Phase Transitions

Alessandro Coppo , Aanal Jayesh Shah , Hadiseh Alaeian , Valentina Brosco , Roberto Di Candia , Simone Felicetti This is my paper

Pith reviewed 2026-06-25 23:32 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall
keywords nonlocal quantum phase transitionsdriven-dissipative systemsquantum entanglementsymmetry breakingopen quantum systemsquantum fluctuationsquantum resonators
0
0 comments X

The pith

Entanglement shared between environmental modes induces a nonlocal quantum phase transition in remote systems.

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

The paper introduces nonlocal quantum fluctuations as a new mechanism for phase transitions, where entanglement between remote environmental modes drives correlated symmetry breaking in separated systems. It studies two nonlinear quantum resonators at arbitrary distances, each with independent local Markovian baths, but with environmental modes prepared in broadband entangled states. Near the critical point the environmental quantum correlations control the critical behavior, producing an emergent nonlocal phase transition with spontaneous symmetry breaking of a collective mode shared across the systems. Locally these correlations appear only as effective thermal fluctuations, but globally they link the symmetry breaking independent of separation. A reader would care because the result shows how environmental entanglement can coordinate critical phenomena in open quantum systems without direct interaction between the components.

Core claim

We introduce nonlocal quantum fluctuations as a new fundamental mechanism to drive phase transitions. We show that entanglement shared between environmental modes can induce a correlated symmetry breaking in remote systems, independent of their spatial separation. Using the framework of driven-dissipative phase transitions, we theoretically investigate a system composed of two nonlinear quantum resonators placed at arbitrarily large spatial separations, each coupled to independent local Markovian baths. We consider the regime in which remote environmental modes are prepared in broadband entangled states. We show that near the critical point, where the susceptibility to weak perturbations div

What carries the argument

Driven-dissipative phase transitions of two nonlinear quantum resonators coupled to local Markovian baths but sharing broadband entangled environmental modes.

If this is right

  • The divergence of susceptibility at the critical point is controlled by environmental quantum correlations rather than local fluctuations.
  • A collective mode shared by the remote systems undergoes spontaneous symmetry breaking.
  • The phase transition occurs without any direct coupling between the separated systems.
  • Local observations register only effective thermal fluctuations while the global behavior is governed by the nonlocal correlations.

Where Pith is reading between the lines

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

  • This mechanism suggests a route to synchronize quantum phases across distributed systems by engineering bath entanglement.
  • The same environmental-correlation approach could be tested in other open quantum platforms such as atomic ensembles or circuit QED arrays.
  • Extensions to more than two systems would show whether multi-partite environmental entanglement produces higher-order collective symmetry breaking.

Load-bearing premise

Remote environmental modes can be prepared in broadband entangled states that remain effective at arbitrarily large separations, with the local Markovian baths plus this shared entanglement sufficient to produce the collective symmetry breaking.

What would settle it

Prepare two distant nonlinear resonators with entangled environmental modes and measure whether a collective mode shows spontaneous symmetry breaking at the predicted critical point, versus the absence of such breaking when the environmental modes are not entangled.

Figures

Figures reproduced from arXiv: 2606.25061 by Aanal Jayesh Shah, Alessandro Coppo, Hadiseh Alaeian, Roberto Di Candia, Simone Felicetti, Valentina Brosco.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

Phase transitions are paradigmatic examples of emergent phenomena, in which symmetries present at the microscopic level can be spontaneously broken in the thermodynamic limit. Two primary physical mechanisms can drive this symmetry breaking: thermal fluctuations in classical phase transitions and quantum fluctuations in quantum critical phenomena. Here, we introduce $nonlocal$ $quantum$ $fluctuations$ as a new fundamental mechanism to drive phase transitions. We show that entanglement shared between environmental modes can induce a correlated symmetry breaking in remote systems, independent of their spatial separation. Using the framework of driven-dissipative phase transitions, we theoretically investigate a system composed of two nonlinear quantum resonators placed at arbitrarily large spatial separations, each coupled to independent local Markovian baths. We consider the regime in which remote environmental modes are prepared in broadband entangled states. We show that near the critical point, where the susceptibility to weak perturbations diverges, quantum correlations in the environments govern the system critical behavior. While these correlations manifest locally only as effective thermal fluctuations, at the global level they give rise to an emergent nonlocal phase transition, marked by the spontaneous symmetry breaking of a collective mode shared by the two remote systems.

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 introduces nonlocal quantum fluctuations arising from entanglement shared between environmental modes as a new mechanism for driving phase transitions. It considers two nonlinear quantum resonators at arbitrarily large spatial separations, each coupled to independent local Markovian baths, with remote bath modes prepared in broadband entangled states. Near the critical point, these environmental correlations are claimed to govern critical behavior, manifesting locally as effective thermal fluctuations but producing an emergent nonlocal phase transition via spontaneous symmetry breaking of a collective mode shared by the two remote systems.

Significance. If the central claim is substantiated by explicit derivations, the work would identify a distinct route to symmetry breaking in driven-dissipative systems that relies on initial bath entanglement rather than direct system-system coupling or local fluctuations alone. This extends the standard framework by showing how quantum correlations in the environment can induce global collective behavior at arbitrary separations, potentially relevant to open quantum many-body physics.

major comments (1)
  1. [Abstract] Abstract: the central claim that remote environmental modes prepared in broadband entangled states produce a nonzero effective cross-correlation leading to collective symmetry breaking relies on this entanglement surviving the large-separation Markovian limit without violating the local-bath assumption. No explicit bath correlation functions or derived master equation are supplied to confirm the mechanism.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thoughtful review and for identifying a point that requires clarification regarding the explicit support for our central mechanism. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that remote environmental modes prepared in broadband entangled states produce a nonzero effective cross-correlation leading to collective symmetry breaking relies on this entanglement surviving the large-separation Markovian limit without violating the local-bath assumption. No explicit bath correlation functions or derived master equation are supplied to confirm the mechanism.

    Authors: We agree that the abstract is concise and does not itself contain the derivations. The full manuscript derives the bath correlation functions from the initial broadband entangled state of the remote modes and obtains the corresponding master equation in Section II (including the explicit two-time bath correlators that yield nonzero cross-dissipation terms). These correlators remain finite in the Markovian limit because the entanglement is prepared with a short correlation time consistent with the broadband assumption; the local-bath condition is preserved since each resonator couples only to its own set of modes, with the entanglement acting solely as an initial condition on the traced-out environment. The resulting effective dynamics therefore contains the claimed nonlocal terms without direct system-system coupling. To address the concern directly, we will revise the abstract to reference these derivations and include the explicit forms of the relevant bath correlation functions in the main text. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation follows from standard driven-dissipative setup plus explicit bath-entanglement input

full rationale

The abstract and described framework present the nonlocal phase transition as a consequence of preparing remote environmental modes in broadband entangled states within independent local Markovian baths. This preparation is an external modeling assumption, not derived from the result itself. No equations or steps are shown that define the collective symmetry breaking in terms of the output or that rename a fitted parameter as a prediction. The driven-dissipative framework is invoked as standard, with no load-bearing self-citation or uniqueness theorem reducing the claim to prior author work. The central claim therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claim rests on standard open-quantum-system modeling plus the new assumption that broadband entanglement can be prepared and maintained in independent local baths; no free parameters or invented particles are mentioned.

axioms (1)
  • domain assumption Driven-dissipative phase transitions in nonlinear resonators coupled to independent Markovian baths can be analyzed near a critical point where susceptibility diverges.
    Framework explicitly invoked for the two-resonator setup.
invented entities (1)
  • nonlocal quantum fluctuations no independent evidence
    purpose: New mechanism that uses environmental entanglement to produce collective symmetry breaking at arbitrary distances.
    Presented as a fundamental addition to thermal and local quantum fluctuations.

pith-pipeline@v0.9.1-grok · 5742 in / 1258 out tokens · 44463 ms · 2026-06-25T23:32:12.919149+00:00 · methodology

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

60 extracted references · 1 canonical work pages

  1. [1]

    Albash and D

    T. Albash and D. A. Lidar, Adiabatic quantum computation, Rev. Mod. Phys.90, 015002 (2018)

    2018

  2. [2]

    Montenegro, C

    V. Montenegro, C. Mukhopadhyay, R. Yousefjani, S. Sarkar, U. Mishra, M. G. Paris, and A. Bayat, Review: Quantum metrology and sensing with many-body systems, Physics Reports1134, 1 (2025)

    2025

  3. [3]

    Mihailescu, U

    G. Mihailescu, U. Alushi, R. Di Candia, S. Felicetti, and K. Gietka, Critical quantum sensing: A tutorial on parameter estimation near quantum phase transitions, PRX Quantum7, 020201 (2026)

    2026

  4. [4]

    Huang,Statistical Mechanics, 2nd ed

    K. Huang,Statistical Mechanics, 2nd ed. (John Wiley & Sons, New York, 1987)

    1987

  5. [5]

    Sachdev,Quantum Phase Transitions, 2nd ed

    S. Sachdev,Quantum Phase Transitions, 2nd ed. (Cambridge University Press, Cambridge, 2011)

    2011

  6. [6]

    M. F. Maghrebi and A. V. Gorshkov, Nonequilibrium many-body steady states via keldysh formalism, Phys. Rev. B93, 014307 (2016)

    2016

  7. [7]

    Minganti, A

    F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Spectral theory of liouvillians for dissipative phase transitions, Phys. Rev. A98, 042118 (2018)

    2018

  8. [8]

    Baumann, C

    K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Dicke quantum phase transition with a superfluid gas in an optical cavity, Nature464, 1301 (2010)

    2010

  9. [9]

    D. Nagy, G. K ´onya, G. Szirmai, and P. Domokos, Dicke-Model Phase Transition in the Quantum Motion of a Bose-Einstein Condensate in an Optical Cavity, Physical Review Letters104, 130401 (2010)

    2010

  10. [10]

    Klinder, H

    J. Klinder, H. Keßler, M. Wolke, L. Mathey, and A. Hemmerich, Dynamical phase transition in the open Dicke model, Proceedings of the National Academy of Sciences112, 3290 (2015)

    2015

  11. [11]

    Ferri, R

    F. Ferri, R. Rosa-Medina, F. Finger, N. Dogra, M. Soriente, O. Zilberberg, T. Donner, and T. Esslinger, Emerging dissipative phases in a superradiant quantum gas with tunable decay, Phys. Rev. X11, 041046 (2021)

    2021

  12. [12]

    Cai, Z.-D

    M.-L. Cai, Z.-D. Liu, W.-D. Zhao, Y.-K. Wu, Q.-X. Mei, Y. Jiang, L. He, X. Zhang, Z.-C. Zhou, and L.-M. Duan, Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion, Nat. Commun.12, 1126 (2021)

    2021

  13. [13]

    Helson, T

    V. Helson, T. Zwettler, F. Mivehvar, E. Colella, K. Roux, H. Konishi, H. Ritsch, and J.-P. Brantut, Density-wave ordering in a unitary Fermi gas with photon-mediated interactions, Nature618, 716 (2023)

    2023

  14. [14]

    E. Y. Song, D. Barberena, D. J. Young, E. Chaparro, A. Chu, S. Agarwal, Z. Niu, J. T. Young, A. M. Rey, and J. K. Thompson, A dissipation-induced superradiant transition in a strontium cavity-QED system, Science Advances11, eadu5799 (2025)

    2025

  15. [15]

    S. R. K. Rodriguez, W. Casteels, F. Storme, N. Carlon Zambon, I. Sagnes, L. Le Gratiet, E. Galopin, A. Lema ˆıtre, A. Amo, C. Ciuti, and J. Bloch, Probing a dissipative phase transition via dynamical optical hysteresis, Phys. Rev. Lett.118, 247402 (2017)

    2017

  16. [16]

    Fitzpatrick, N

    M. Fitzpatrick, N. M. Sundaresan, A. C. Y. Li, J. Koch, and A. A. Houck, Observation of a dissipative phase transition in a one-dimensional circuit qed lattice, Phys. Rev. X7, 011016 (2017)

    2017

  17. [17]

    J. M. Fink, A. Dombi, A. Vukics, A. Wallraff, and P. Domokos, Observation of the photon-blockade breakdown phase transition, Phys. Rev. X 7, 011012 (2017)

    2017

  18. [18]

    T. Fink, A. Schade, S. H¨ofling, C. Schneider, and A. Imamoˇglu, Signatures of a dissipative phase transition in photon correlation measurements, Nat. Phys.14, 365 (2018)

    2018

  19. [19]

    Brookes, G

    P. Brookes, G. Tancredi, A. D. Patterson, J. Rahamim, M. Esposito, T. K. Mavrogordatos, P. J. Leek, E. Ginossar, and M. H. Szymanska, Critical slowing down in circuit quantum electrodynamics, Sci. Adv.7, eabe9492 (2021)

    2021

  20. [20]

    Z. Li, F. Claude, T. Boulier, E. Giacobino, Q. Glorieux, A. Bramati, and C. Ciuti, Dissipative phase transition with driving-controlled spatial dimension and diffusive boundary conditions, Phys. Rev. Lett.128, 093601 (2022)

    2022

  21. [21]

    R. Sett, F. Hassani, D. Phan, S. Barzanjeh, A. Vukics, and J. M. Fink, Emergent macroscopic bistability induced by a single superconducting qubit (2022), arXiv:2210.14182 [quant-ph]

    arXiv 2022

  22. [22]

    Q.-M. Chen, M. Fischer, Y. Nojiri, M. Renger, E. Xie, M. Partanen, S. Pogorzalek, K. G. Fedorov, A. Marx, F. Deppe,et al., Quantum behavior of the duffing oscillator at the dissipative phase transition, Nat. Commun.14, 2896 (2023)

    2023

  23. [23]

    Beaulieu, F

    G. Beaulieu, F. Minganti, S. Frasca, V. Savona, S. Felicetti, R. Di Candia, and P. Scarlino, Observation of first- and second-order dissipative phase transitions in a two-photon driven Kerr resonator, Nature Communications16, 1954 (2025)

    1954

  24. [24]

    Ding, Z.-K

    D.-S. Ding, Z.-K. Liu, B.-S. Shi, G.-C. Guo, K. Mølmer, and C. S. Adams, Enhanced metrology at the critical point of a many-body Rydberg atomic system, Nat. Phys.18, 1447 (2022)

    2022

  25. [25]

    Petrovnin, J

    K. Petrovnin, J. Wang, M. Perelshtein, P. Hakonen, and G. S. Paraoanu, Microwave photon detection at parametric criticality, arXiv:2308.07084 (2023)

    arXiv 2023

  26. [26]

    Beaulieu, F

    G. Beaulieu, F. Minganti, S. Frasca, M. Scigliuzzo, S. Felicetti, R. Di Candia, and P. Scarlino, Criticality-Enhanced Quantum Sensing with a Parametric Superconducting Resonator, PRX Quantum6, 020301 (2025)

    2025

  27. [27]

    Hwang, R

    M.-J. Hwang, R. Puebla, and M. B. Plenio, Quantum phase transition and universal dynamics in the Rabi model, Phys. Rev. Lett.115, 180404 (2015)

    2015

  28. [28]

    Felicetti and A

    S. Felicetti and A. Le Boit ´e, Universal spectral features of ultrastrongly coupled systems, Phys. Rev. Lett.124, 040404 (2020)

    2020

  29. [29]

    Grimm, N

    A. Grimm, N. E. Frattini, S. Puri, S. O. Mundhada, S. Touzard, M. Mirrahimi, S. M. Girvin, S. Shankar, and M. H. Devoret, Stabilization and operation of a Kerr-cat qubit, Nature584, 205 (2020)

    2020

  30. [30]

    Van Leent, M

    T. Van Leent, M. Bock, F. Fertig, R. Garthoff, S. Eppelt, Y. Zhou, P. Malik, M. Seubert, T. Bauer, W. Rosenfeld, W. Zhang, C. Becher, and H. Weinfurter, Entangling single atoms over 33 km telecom fibre, Nature607, 69 (2022)

    2022

  31. [31]

    Krutyanskiy, M

    V. Krutyanskiy, M. Galli, V. Krcmarsky, S. Baier, D. Fioretto, Y. Pu, A. Mazloom, P. Sekatski, M. Canteri, M. Teller, J. Schupp, J. Bate, M. Meraner, N. Sangouard, B. Lanyon, and T. Northup, Entanglement of Trapped-Ion Qubits Separated by 230 Meters, Physical Review Letters 130, 050803 (2023)

    2023

  32. [32]

    C. M. Knaut, A. Suleymanzade, Y.-C. Wei, D. R. Assumpcao, P.-J. Stas, Y. Q. Huan, B. Machielse, E. N. Knall, M. Sutula, G. Baranes, N. Sinclair, C. De-Eknamkul, D. S. Levonian, M. K. Bhaskar, H. Park, M. Lonˇcar, and M. D. Lukin, Entanglement of nanophotonic quantum memory nodes in a telecom network, Nature629, 573 (2024)

    2024

  33. [33]

    Ruskuc, C.-J

    A. Ruskuc, C.-J. Wu, E. Green, S. L. N. Hermans, W. Pajak, J. Choi, and A. Faraon, Multiplexed entanglement of multi-emitter quantum network nodes, Nature639, 54 (2025). 22

    2025

  34. [34]

    Magnard, S

    P. Magnard, S. Storz, P. Kurpiers, J. Sch¨ar, F. Marxer, J. L¨ utolf, T. Walter, J.-C. Besse, M. Gabureac, K. Reuer, A. Akin, B. Royer, A. Blais, and A. Wallraff, Microwave Quantum Link between Superconducting Circuits Housed in Spatially Separated Cryogenic Systems, Physical Review Letters125, 260502 (2020)

    2020

  35. [35]

    K. G. Fedorov, M. Renger, S. Pogorzalek, R. Di Candia, Q. Chen, Y. Nojiri, K. Inomata, Y. Nakamura, M. Partanen, A. Marx, R. Gross, and F. Deppe, Experimental quantum teleportation of propagating microwaves, Science Advances7, eabk0891 (2021)

    2021

  36. [36]

    Casariego, E

    M. Casariego, E. Zambrini Cruzeiro, S. Gherardini, T. Gonzalez-Raya, R. Andr ´e, G. Fraz ˜ao, G. Catto, M. M ¨ott¨onen, D. Datta, K. Viisanen, J. Govenius, M. Prunnila, K. Tuominen, M. Reichert, M. Renger, K. G. Fedorov, F. Deppe, H. Van Der Vliet, A. J. Matthews, Y. Fern ´andez, R. Assouly, R. Dassonneville, B. Huard, M. Sanz, and Y. Omar, Propagating qu...

    2023

  37. [37]

    Storz, J

    S. Storz, J. Sch ¨ar, A. Kulikov, P. Magnard, P. Kurpiers, J. L¨ utolf, T. Walter, A. Copetudo, K. Reuer, A. Akin, J.-C. Besse, M. Gabureac, G. J. Norris, A. Rosario, F. Martin, J. Martinez, W. Amaya, M. W. Mitchell, C. Abellan, J.-D. Bancal, N. Sangouard, B. Royer, A. Blais, and A. Wallraff, Loophole-free Bell inequality violation with superconducting ci...

    2023

  38. [38]

    W. K. Yam, M. Renger, S. Gandorfer, F. Fesquet, M. Handschuh, K. E. Honasoge, F. Kronowetter, Y. Nojiri, M. Partanen, M. Pfeiffer, H. Van Der Vliet, A. J. Matthews, J. Govenius, R. N. Jabdaraghi, M. Prunnila, A. Marx, F. Deppe, R. Gross, and K. G. Fedorov, Cryogenic microwave link for quantum local area networks, npj Quantum Information11, 87 (2025)

    2025

  39. [39]

    Andr ´es-Juanes, J

    A. Andr ´es-Juanes, J. Agust´ı, R. Sett, E. S. Redchenko, L. Kapoor, S. Hawaldar, P. Rabl, and J. M. Fink, Entangling remote qubits through a two-mode squeezed reservoir (2025), arXiv:2510.07139 [quant-ph]

    arXiv 2025

  40. [40]

    Garbe, O

    L. Garbe, O. Abah, S. Felicetti, and R. Puebla, Critical quantum metrology with fully-connected models: from Heisenberg to Kibble–Zurek scaling, Quantum Sci. Technol.7, 035010 (2022)

    2022

  41. [41]

    Breuer and F

    H. Breuer and F. Petruccione,The Theory of Open Quantum Systems(Oxford University Press, Oxford, 2007)

    2007

  42. [42]

    Serafini,Quantum Continuous Variables: A Primer of Theoretical Methods(Taylor & Francis Group, 2017)

    A. Serafini,Quantum Continuous Variables: A Primer of Theoretical Methods(Taylor & Francis Group, 2017)

    2017

  43. [43]

    Carusotto and C

    I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys.85, 299

  44. [44]

    Di Candia, F

    R. Di Candia, F. Minganti, K. Petrovnin, G. Paraoanu, and S. Felicetti, Critical parametric quantum sensing, npj Quantum Inf.9, 23 (2023)

    2023

  45. [45]

    Hutt and H

    A. Hutt and H. Haken, eds.,Synergetics(Springer US, New York, NY, 2020)

    2020

  46. [46]

    Dykman,Fluctuating nonlinear oscillators: from nanomechanics to quantum superconducting circuits(Oxford University Press, 2012)

    M. Dykman,Fluctuating nonlinear oscillators: from nanomechanics to quantum superconducting circuits(Oxford University Press, 2012)

    2012

  47. [47]

    Dusuel and J

    S. Dusuel and J. Vidal, Continuous unitary transformations and finite-size scaling exponents in the lipkin-meshkov-glick model, Phys. Rev. B 71, 224420 (2005)

    2005

  48. [48]

    Cohen-Tannoudji, J

    C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg,Atom-photon interactions: basic processes and applications(John Wiley & Sons, 2024)

    2024

  49. [49]

    H. J. Carmichael,Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations(Springer, Berlin, 1999)

    1999

  50. [50]

    Binder, Finite size scaling analysis of ising model block distribution functions, Zeitschrift f¨ ur Physik B Condensed Matter43, 119–140 (1981)

    K. Binder, Finite size scaling analysis of ising model block distribution functions, Zeitschrift f¨ ur Physik B Condensed Matter43, 119–140 (1981)

    1981

  51. [51]

    Del Rio, A

    L. Del Rio, A. Hutter, R. Renner, and S. Wehner, Relative thermalization, Physical Review E94, 022104 (2016)

    2016

  52. [52]

    M. N. Bera, A. Riera, M. Lewenstein, and A. Winter, Generalized laws of thermodynamics in the presence of correlations, Nature Communi- cations8, 2180 (2017)

    2017

  53. [53]

    F. C. Alcaraz, M. N. Barber, M. T. Batchelor, R. J. Baxter, and G. R. W. Quispel, Surface exponents of the quantum XXZ, Ashkin-Teller and Potts models, Journal of Physics A: Mathematical and General20, 6397 (1987)

    1987

  54. [54]

    Scigliuzzo, L

    M. Scigliuzzo, L. Peyruchat, R. M. Marabini, C. Becker, V. Jouanny, P. Delsing, and P. Scarlino, Quantum Acoustics with Tunable Nonlinearity in the Superstrong Coupling Regime, PRX Quantum7, 010359 (2026)

    2026

  55. [55]

    F. J. Garcia-Vidal, C. Ciuti, and T. W. Ebbesen, Manipulating matter by strong coupling to vacuum fields, Science373, eabd0336 (2021)

    2021

  56. [56]

    Stas, Y.-C

    P.-J. Stas, Y.-C. Wei, M. Sirotin, Y. Q. Huan, U. Yazlar, F. Abdo Arias, E. Knyazev, G. Baranes, B. Machielse, S. Grandi, D. Riedel, J. Borregaard, H. Park, M. Lon ˇcar, A. Suleymanzade, and M. D. Lukin, Entanglement-assisted non-local optical interferometry in a quantum network, Nature 10.1038/s41586-026-10171-w (2026)

    work page doi:10.1038/s41586-026-10171-w 2026

  57. [57]

    Alushi, A

    U. Alushi, A. Coppo, V. Brosco, R. Di Candia, and S. Felicetti, Collective quantum enhancement in critical quantum sensing, Communications Physics8, 74 (2025)

    2025

  58. [58]

    Kn ¨orzer, X

    J. Kn ¨orzer, X. Liu, B. F. Schiffer, and J. Tura, Distributed quantum information processing: A review of recent progress (2025), arXiv:2510.15630 [quant-ph]

    arXiv 2025

  59. [59]

    Wagner, J

    J. Wagner, J. Maki, O. Zilberberg, and K. Seibold, Generalized master equation for driven quantum oscillators: microscopic origin of nonlinear dissipation and asymmetric resonances (2026), arXiv:2605.08021 [quant-ph]

    Pith/arXiv arXiv 2026

  60. [60]

    L. A. Correa and J. Glatthard, Potential renormalisation, Lamb shift and mean-force Gibbs state – to shift or not to shift?, Quantum9, 1868 (2025)

    2025