- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Information transport and transport-induced entanglement in open fermion chains

Andrea Nava1,*, Claudia Artiaco2,3, Yuval Gefen4, Igor Gornyi5,6, Mikheil Tsitsishvili1, Alex Zazunov1, and Reinhold Egger1

  • *Contact author: a.nava@hhu.de
PDF

Phys. Rev. Research 8, 033273 – Published 3 September, 2026

DOI: https://doi.org/10.1103/5dks-395l

Abstract

Understanding the entanglement dynamics in quantum many-body systems under steady-state transport conditions is an actively pursued challenging topic. Hydrodynamic equations, akin to transport equations for charge or heat, would be of great interest but face severe challenges because of the inherent nonlocality of entanglement and the difficulty of identifying conservation laws. We show that progress is facilitated by using information as a key quantity related to—but distinct from—entanglement. Employing the recently developed “information lattice” framework, we formulate general continuity equations governing the flow of spatially and scale-resolved information currents in nonequilibrium open quantum systems. To illustrate our theory, we consider noninteracting fermion chains coupled to dissipative reservoirs, using Lindblad master equations. By relating the information lattice to a noise lattice constructed from particle-number fluctuations, we show that information is experimentally accessible via noise measurements. Similarly, local information currents can be obtained by measuring particle currents, on-site occupations, and covariances of particle numbers and/or particle currents. Using the fermionic negativity to quantify bipartite entanglement, we also study transport-induced entanglement and its relation to information currents. For a clean particle-hole symmetric chain, we find that information currents are shielded from entering the information lattice. Impurities or particle-hole asymmetry break this effect, causing information current flow and entanglement between end segments of the chain. Our work opens the door to systematic investigations of information transport and entanglement generation in driven open quantum systems far from equilibrium.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (149)

  1. C. H. Bennett and D. P. DiVincenzo, Quantum information and computation, Nature (London) 404, 247 (2000).
  2. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
  3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2010).
  4. M. Wilde, Quantum Information Theory (Cambridge University Press, Cambridge, UK, 2013).
  5. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80, 517 (2008).
  6. J. I. Cirac, Entanglement in many-body quantum systems, arXiv:1205.3742.
  7. N. Laflorencie, Quantum entanglement in condensed matter systems, Phys. Rep. 646, 1 (2016).
  8. B. Zeng, X. Chen, D.-L. Zhou, and X.-G. Wen, Quantum Information Meets Quantum Matter (Springer, New York, 2019).
  9. J. Eisert, M. Cramer, and M. B. Plenio, Colloquium: Area laws for the entanglement entropy, Rev. Mod. Phys. 82, 277 (2010).
  10. M. Srednicki, Entropy and area, Phys. Rev. Lett. 71, 666 (1993).
  11. M. B. Hastings, An area law for one-dimensional quantum systems, J. Stat. Mech. (2007) P08024.
  12. M. M. Wolf, F. Verstraete, M. B. Hastings, and J. I. Cirac, Area laws in quantum systems: Mutual information and correlations, Phys. Rev. Lett. 100, 070502 (2008).
  13. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Entanglement in quantum critical phenomena, Phys. Rev. Lett. 90, 227902 (2003).
  14. P. Calabrese and J. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. (2005) P04010.
  15. K. Kobayashi, Time evolution of the von Neumann entropy in open quantum system, arXiv:2405.11824.
  16. H. Cheraghi, A. G. Moghaddam, and T. Ojanen, Entanglement-limited linear response in fermionic systems, arXiv:2511.19415.
  17. A. Hamma, R. Ionicioiu, and P. Zanardi, Ground state entanglement and geometric entropy in the Kitaev model, Phys. Lett. A 337, 22 (2005).
  18. A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96, 110404 (2006).
  19. M. Levin and X.-G. Wen, Detecting topological order in a ground state wave function, Phys. Rev. Lett. 96, 110405 (2006).
  20. M. B. Hastings, Topological order at nonzero temperature, Phys. Rev. Lett. 107, 210501 (2011).
  21. L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
  22. R. Fan, Y. Bao, E. Altman, and A. Vishwanath, Diagnostics of mixed-state topological order and breakdown of quantum memory, PRX Quantum 5, 020343 (2024).
  23. S. Sang, Y. Zou, and T. H. Hsieh, Mixed-state quantum phases: Renormalization and quantum error correction, Phys. Rev. X 14, 031044 (2024).
  24. S. Sang, L. A. Lessa, R. S. K. Mong, T. Grover, C. Wang, and T. H. Hsieh, Mixed-state phases from local reversibility, arXiv:2507.02292.
  25. S. Mas-Mendoza, R. D. P. East, M. Filippone, and A. G. Grushin, A graphical diagnostic of topological order using ZX calculus, arXiv:2509.12355.
  26. B. Kraus, H. P. Büchler, S. Diehl, A. Kantian, A. Micheli, and P. Zoller, Preparation of entangled states by quantum Markov processes, Phys. Rev. A 78, 042307 (2008).
  27. F. Galve, D. Zueco, G. M. Reuther, S. Kohler, and P. Hänggi, Creation and manipulation of entanglement in spin chains far from equilibrium, Eur. Phys. J. Spec. Top. 180, 237 (2009).
  28. D. Zueco, F. Galve, S. Kohler, and P. Hänggi, Quantum router based on ac control of qubit chains, Phys. Rev. A 80, 042303 (2009).
  29. S. Sarkar, Perfect entanglement transport in quantum spin chain systems, J. Quantum Inf. Sci. 01, 105 (2011).
  30. F. Verstraete, M. M. Wolf, and J. Ignacio Cirac, Quantum computation and quantum-state engineering driven by dissipation, Nat. Phys. 5, 633 (2009).
  31. V. Vedral, Entanglement production in non-equilibrium thermodynamics, J. Phys.: Conf. Ser. 143, 012010 (2009).
  32. T. Scholak, F. Mintert, T. Wellens, and A. Buchleitner, Transport and entanglement, in Quantum Efficiency in Complex Systems, Part I: Biomolecular systems, Semiconductors and Semimetals, edited by E. R. Weber, M. Thorwart, and U. Würfel (Elsevier, Amsterdam, 2010), Chap. 1, Vol. 83.
  33. B. Swingle, Entanglement renormalization and holography, Phys. Rev. D 86, 065007 (2012).
  34. M. Nozaki, T. Numasawa, and T. Takayanagi, Holographic local quenches and entanglement density, J. High Energy Phys. 05 (2013) 080.
  35. Y. Lin, J. P. Gaebler, F. Reiter, T. R. Tan, R. Bowler, A. S. Sørensen, D. Leibfried, and D. J. Wineland, Dissipative production of a maximally entangled steady state of two quantum bits, Nature (London) 504, 415 (2013).
  36. S. Shankar, M. Hatridge, Z. Leghtas, K. M. Sliwa, A. Narla, U. Vool, S. M. Girvin, L. Frunzio, M. Mirrahimi, and M. H. Devoret, Autonomously stabilized entanglement between two superconducting quantum bits, Nature (London) 504, 419 (2013).
  37. L. Aolita, F. de Melo, and L. Davidovich, Open-system dynamics of entanglement: A key issues review, Rep. Prog. Phys. 78, 042001 (2015).
  38. R. Mahajan, C. D. Freeman, S. Mumford, N. Tubman, and B. Swingle, Entanglement structure of non-equilibrium steady states, arXiv:1608.05074.
  39. F. Brange, O. Malkoc, and P. Samuelsson, Minimal entanglement witness from electrical current correlations, Phys. Rev. Lett. 118, 036804 (2017).
  40. A. Nahum, J. Ruhman, S. Vijay, and J. Haah, Quantum entanglement growth under random unitary dynamics, Phys. Rev. X 7, 031016 (2017).
  41. C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi, Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws, Phys. Rev. X 8, 021013 (2018).
  42. C. K. Lee, M. S. Najafabadi, D. Schumayer, L. C. Kwek, and D. A. W. Hutchinson, Environment mediated multipartite and multidimensional entanglement, Sci. Rep. 9, 9147 (2019).
  43. X. Cao, A. Tilloy, and A. De Luca, Entanglement in a fermion chain under continuous monitoring, SciPost Phys. 7, 024 (2019).
  44. V. Alba, B. Bertini, and M. Fagotti, Entanglement evolution and generalised hydrodynamics: Interacting integrable systems, SciPost Phys. 7, 005 (2019).
  45. A. Panda and S. Banerjee, Entanglement in nonequilibrium steady states and many-body localization breakdown in a current-driven system, Phys. Rev. B 101, 184201 (2020).
  46. P. Sancho, Continuity equations for entanglement, arXiv:2006.08377.
  47. I. V. Vovcenko, V. Y. Shishkov, and E. S. Andrianov, Dephasing-assisted entanglement in a system of strongly coupled qubits, Opt. Express 29, 9685 (2021).
  48. O. Alberton, M. Buchhold, and S. Diehl, Entanglement transition in a monitored free-fermion chain: From extended criticality to area law, Phys. Rev. Lett. 126, 170602 (2021).
  49. S. Fraenkel and M. Goldstein, Entanglement measures in a nonequilibrium steady state: Exact results in one dimension, SciPost Phys. 11, 085 (2021).
  50. T. Klein Kvorning, L. Herviou, and J. H. Bardarson, Time-evolution of local information: Thermalization dynamics of local observables, SciPost Phys. 13, 080 (2022).
  51. P. Ruggiero, P. Calabrese, B. Doyon, and J. Dubail, Quantum generalized hydrodynamics of the Tonks–Girardeau gas: Density fluctuations and entanglement entropy, J. Phys. A 55, 024003 (2022).
  52. B. Bertini, K. Klobas, V. Alba, G. Lagnese, and P. Calabrese, Growth of Rényi entropies in interacting integrable models and the breakdown of the quasiparticle picture, Phys. Rev. X 12, 031016 (2022).
  53. F. Carollo and V. Alba, Entangled multiplets and spreading of quantum correlations in a continuously monitored tight-binding chain, Phys. Rev. B 106, L220304 (2022).
  54. V. Alba and F. Carollo, Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case, SciPost Phys. 15, 124 (2023).
  55. S. Fraenkel and M. Goldstein, Extensive long-range entanglement in a nonequilibrium steady state, SciPost Phys. 15, 134 (2023).
  56. C. Muzzi, M. Tsitsishvili, and G. Chiriacò, Entanglement enhancement induced by noise in inhomogeneously monitored systems, Phys. Rev. B 111, 014312 (2025).
  57. C. Tan, Y. Hang, S. Haas, and H. Saleur, Entanglement flow in the Kane-Fisher quantum impurity problem, SciPost Phys. Core 8, 002 (2025).
  58. E. Tirrito, P. S. Tarabunga, D. S. Bhakuni, M. Dalmonte, P. Sierant, and X. Turkeshi, Universal spreading of nonstabilizerness and quantum transport, arXiv:2506.12133.
  59. I. Poboiko and A. D. Mirlin, Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transitions, Phys. Rev. B 113, 144311 (2026).
  60. D. Shekhar and P. Shukla, Single-particle entanglement dynamics in complex systems, Entropy 28, 29 (2026).
  61. C. Jonay, D. A. Huse, and A. Nahum, Coarse-grained dynamics of operator and state entanglement, arXiv:1803.00089.
  62. T. Zhou and A. Nahum, Entanglement membrane in chaotic many-body systems, Phys. Rev. X 10, 031066 (2020).
  63. M. Mezei, Membrane theory of entanglement dynamics from holography, Phys. Rev. D 98, 106025 (2018).
  64. M. Mezei and J. Virrueta, Exploring the membrane theory of entanglement dynamics, J. High Energy Phys. 02 (2020) 013.
  65. H. Liu and S. J. Suh, Entanglement tsunami: Universal scaling in holographic thermalization, Phys. Rev. Lett. 112, 011601 (2014).
  66. P. C. Martin, E. D. Siggia, and H. A. Rose, Statistical dynamics of classical systems, Phys. Rev. A 8, 423 (1973).
  67. S. Gopalakrishnan, E. McCulloch, and R. Vasseur, Monitored fluctuating hydrodynamics, Phys. Rev. X 16, 011024 (2026).
  68. J. Hauser, K. Su, H. Ha, J. Lloyd, T. G. Kiely, R. Vasseur, S. Gopalakrishnan, C. Xu, and M. P. A. Fisher, Strong-to-weak symmetry breaking in open quantum systems: From discrete particles to continuum hydrodynamics, arXiv:2602.16045.
  69. H. Shapourian, K. Shiozaki, and S. Ryu, Partial time-reversal transformation and entanglement negativity in fermionic systems, Phys. Rev. B 95, 165101 (2017).
  70. H. Shapourian, K. Shiozaki, and S. Ryu, Many-body topological invariants for fermionic symmetry-protected topological phases, Phys. Rev. Lett. 118, 216402 (2017).
  71. H. Shapourian and S. Ryu, Finite-temperature entanglement negativity of free fermions, J. Stat. Mech. (2019) 043106.
  72. H. Shapourian and S. Ryu, Entanglement negativity of fermions: Monotonicity, separability criterion, and classification of few-mode states, Phys. Rev. A 99, 022310 (2019).
  73. J. Eisert, V. Eisler, and Z. Zimborás, Entanglement negativity bounds for fermionic Gaussian states, Phys. Rev. B 97, 165123 (2018).
  74. C. Artiaco, T. Klein Kvorning, D. Aceituno Chávez, L. Herviou, and J. H. Bardarson, Universal characterization of quantum many-body states through local information, Phys. Rev. Lett. 134, 190401 (2025).
  75. N. P. Bauer, B. Trauzettel, T. Klein Kvorning, J. H. Bardarson, and C. Artiaco, Local information flow in quantum quench dynamics, Phys. Rev. A 112, 022221 (2025).
  76. I. M. Flór, C. Artiaco, T. K. Kvorning, and J. H. Bardarson, Higher-dimensional information lattice: Quantum state characterization through inclusion-exclusion local information, arXiv:2512.20793.
  77. C. Artiaco, C. Fleckenstein, D. Aceituno Chávez, T. K. Kvorning, and J. H. Bardarson, Efficient large-scale many-body quantum dynamics via local-information time evolution, PRX Quantum 5, 020352 (2024).
  78. K. Harkins, C. Fleckenstein, N. D’Souza, P. M. Schindler, D. Marchiori, C. Artiaco, Q. Reynard-Feytis, U. Basumallick, W. Beatrez, A. Pillai, M. Hagn, A. Nayak, S. Breuer, X. Lv, M. McAllister, P. Reshetikhin, E. Druga, M. Bukov, and A. Ajoy, Nanoscale engineering and dynamic stabilization of mesoscopic spin textures, Sci. Adv. 11, eadn9021 (2025).
  79. C. Artiaco, J. Barata, and E. Rico, Out-of-equilibrium dynamics in a U(1) lattice gauge theory via local information flows: Scattering and string breaking, arXiv:2510.16101.
  80. J. Barata, J. Hormaza, Z.-B. Kang, and W. Qian, Hadronic scattering in (1+1)D SU(2) lattice gauge theory from tensor networks, J. High Energy Phys. 06 (2026) 168.
  81. Y. Bilinskaya, M. F. Martínez, S. Ghosh, T. Klein Kvorning, C. Artiaco, and J. H. Bardarson, Witnessing short- and long-range nonstabilizerness via the information lattice, arXiv:2510.26696.
  82. B. Žunkovič, Closed hierarchy of correlations in Markovian open quantum systems, New J. Phys. 16, 013042 (2014).
  83. T. Barthel and Y. Zhang, Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems, J. Stat. Mech. (2022) 113101.
  84. R. Fazio, J. Keeling, L. Mazza, and M. Schirò, Many-body open quantum systems, SciPost Phys. Lect. Notes 99 (2025).
  85. M. Knap, A. Kantian, T. Giamarchi, I. Bloch, M. D. Lukin, and E. Demler, Probing real-space and time-resolved correlation functions with many-body Ramsey interferometry, Phys. Rev. Lett. 111, 147205 (2013).
  86. J. S. Pedernales, R. Di Candia, I. L. Egusquiza, J. Casanova, and E. Solano, Efficient quantum algorithm for computing n-time correlation functions, Phys. Rev. Lett. 113, 020505 (2014).
  87. L. Del Re, B. Rost, M. Foss-Feig, A. F. Kemper, and J. K. Freericks, Robust measurements of n-point correlation functions of driven-dissipative quantum systems on a digital quantum computer, Phys. Rev. Lett. 132, 100601 (2024).
  88. M. Liu, M. Arzamasovs, Y. Zhang, R. Tian, Z. Li, S. Li, and B. Liu, Many-body interferometry of one-dimensional integrable systems, Phys. Rev. A 111, 053310 (2025).
  89. C.-s. Yu and H. Zhao, Direct measure of quantum correlation, Phys. Rev. A 84, 062123 (2011).
  90. M. Kastner, Ancilla-assisted probing of temporal quantum correlations of large spins, Phys. Rev. A 102, 022212 (2020).
  91. X. Wang, L. Xiong, X. Cai, and X. Yuan, Computing n-time correlation functions without ancilla qubits, Phys. Rev. Lett. 135, 230602 (2025).
  92. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, Oxford, 2007).
  93. P. H. Guimarães, G. T. Landi, and M. J. de Oliveira, Nonequilibrium quantum chains under multisite Lindblad baths, Phys. Rev. E 94, 032139 (2016).
  94. E. G. Cinnirella, A. Nava, G. Campagnano, and D. Giuliano, Phase diagram of the disordered Kitaev chain with long-range pairing connected to external baths, Phys. Rev. B 111, 155149 (2025).
  95. G. Benenti, G. Casati, T. Prosen, D. Rossini, and M. Žnidarič, Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium, Phys. Rev. B 80, 035110 (2009).
  96. C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27, 379 (1948).
  97. A. Nava, M. Rossi, and D. Giuliano, Lindblad equation approach to the determination of the optimal working point in nonequilibrium stationary states of an interacting electronic one-dimensional system: Application to the spinless Hubbard chain in the clean and in the weakly disordered limit, Phys. Rev. B 103, 115139 (2021).
  98. V. Berger, A. Nava, J. H. Bardarson, and C. Artiaco, Numerical study of disordered noninteracting chains coupled to a local Lindblad bath, SciPost Phys. Core 8, 080 (2025).
  99. I. Peschel and V. Eisler, Reduced density matrices and entanglement entropy in free lattice models, J. Phys. A 42, 504003 (2009).
  100. J. Eisert and M. Cramer, Single-copy entanglement in critical quantum spin chains, Phys. Rev. A 72, 042112 (2005).
  101. I. Klich and L. Levitov, Quantum noise as an entanglement meter, Phys. Rev. Lett. 102, 100502 (2009).
  102. H. F. Song, S. Rachel, and K. Le Hur, General relation between entanglement and fluctuations in one dimension, Phys. Rev. B 82, 012405 (2010).
  103. H. F. Song, C. Flindt, S. Rachel, I. Klich, and K. Le Hur, Entanglement entropy from charge statistics: Exact relations for noninteracting many-body systems, Phys. Rev. B 83, 161408 (2011).
  104. H. F. Song, S. Rachel, C. Flindt, I. Klich, N. Laflorencie, and K. Le Hur, Bipartite fluctuations as a probe of many-body entanglement, Phys. Rev. B 85, 035409 (2012).
  105. P. Calabrese, M. Mintchev, and E. Vicari, Exact relations between particle fluctuations and entanglement in Fermi gases, Europhys. Lett. 98, 20003 (2012).
  106. A. Petrescu, H. F. Song, S. Rachel, Z. Ristivojevic, C. Flindt, N. Laflorencie, I. Klich, N. Regnault, and K. Le Hur, Fluctuations and entanglement spectrum in quantum Hall states, J. Stat. Mech. (2014) P10005.
  107. K. H. Thomas and C. Flindt, Entanglement entropy in dynamic quantum-coherent conductors, Phys. Rev. B 91, 125406 (2015).
  108. I. Burmistrov, K. Tikhonov, I. Gornyi, and A. Mirlin, Entanglement entropy and particle number cumulants of disordered fermions, Ann. Phys. (NY) 383, 140 (2017).
  109. I. Poboiko, P. Pöpperl, I. V. Gornyi, and A. D. Mirlin, Theory of free fermions under random projective measurements, Phys. Rev. X 13, 041046 (2023).
  110. I. Poboiko, I. V. Gornyi, and A. D. Mirlin, Measurement-induced phase transition for free fermions above one dimension, Phys. Rev. Lett. 132, 110403 (2024).
  111. R. Süsstrunk and D. A. Ivanov, Free fermions on a line: Asymptotics of the entanglement entropy and entanglement spectrum from full counting statistics, Europhys. Lett. 100, 60009 (2012).
  112. D. A. Ivanov, A. G. Abanov, and V. V. Cheianov, Counting free fermions on a line: A Fisher–Hartwig asymptotic expansion for the Toeplitz determinant in the double-scaling limit, J. Phys. A: Math. Theor. 46, 085003 (2013).
  113. G. Zhang, C. Hong, T. Alkalay, V. Umansky, M. Heiblum, I. Gornyi, and Y. Gefen, Measuring statistics-induced entanglement entropy with a Hong–Ou–Mandel interferometer, Nat. Commun. 15, 3428 (2024).
  114. Note that here we use a convention for the normalization of SA that differs by a factor ln2 from the one in Ref.  [101], where the coefficient relating SA and Var(n̂A) is π2/3.
  115. M. Žnidarič, Exact large-deviation statistics for a nonequilibrium quantum spin chain, Phys. Rev. Lett. 112, 040602 (2014).
  116. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010).
  117. G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi, Quantum tomography, Adv. Imaging Electron Phys. 128, 205 (2003).
  118. R. Islam, R. Ma, P. M. Preiss, M. Eric Tai, A. Lukin, M. Rispoli, and M. Greiner, Measuring entanglement entropy in a quantum many-body system, Nature (London) 528, 77 (2015).
  119. B. Vermersch, M. Ljubotina, J. I. Cirac, P. Zoller, M. Serbyn, and L. Piroli, Many-body entropies and entanglement from polynomially many local measurements, Phys. Rev. X 14, 031035 (2024).
  120. The power-norm color scale employs a power-law transformation to data before mapping it to colors. We use the expression (x−xminxmax−xmin)λ, where [xmin,xmax] is the data range. In all figures, λ=0.3.
  121. Y. V. Nazarov and Y. M. Blanter, Quantum Transport: Introduction to Nanoscience (Cambridge University Press, Cambridge, UK, 2009).
  122. H. Wichterich, M. J. Henrich, H.-P. Breuer, J. Gemmer, and M. Michel, Modeling heat transport through completely positive maps, Phys. Rev. E 76, 031115 (2007).
  123. F. Barra, The thermodynamic cost of driving quantum systems by their boundaries, Sci. Rep. 5, 14873 (2015).
  124. E. Pereira, Heat, work, and energy currents in the boundary-driven XXZ spin chain, Phys. Rev. E 97, 022115 (2018).
  125. L. H. Reis, S. H. S. Silva, and E. Pereira, Beyond the Lindblad master equation: Heat, work, and energy currents in boundary-driven spin chains, Phys. Rev. E 101, 062107 (2020).
  126. N. Cottet, S. Jezouin, L. Bretheau, P. Campagne-Ibarcq, Q. Ficheux, J. Anders, A. Auffèves, R. Azouit, P. Rouchon, and B. Huard, Observing a quantum Maxwell demon at work, Proc. Natl. Acad. Sci. USA 114, 7561 (2017).
  127. A. de Oliveira Junior, J. B. Brask, and P. Lipka-Bartosik, Heat as a witness of quantum properties, Phys. Rev. Lett. 134, 050401 (2025).
  128. B. Xing, G. Chiriacò, P. Cappellaro, R. Fazio, and D. Poletti, Entanglement transition in unitary system-bath dynamics, Phys. Rev. Lett. 136, 240401 (2026).
  129. M. S. Foster and I. L. Aleiner, Slow imbalance relaxation and thermoelectric transport in graphene, Phys. Rev. B 79, 085415 (2009).
  130. X. Turkeshi and M. Schiró, Diffusion and thermalization in a boundary-driven dephasing model, Phys. Rev. B 104, 144301 (2021).
  131. X. Turkeshi, M. Dalmonte, R. Fazio, and M. Schirò, Entanglement transitions from stochastic resetting of non-Hermitian quasiparticles, Phys. Rev. B 105, L241114 (2022).
  132. X. Turkeshi, L. Piroli, and M. Schiró, Enhanced entanglement negativity in boundary-driven monitored fermionic chains, Phys. Rev. B 106, 024304 (2022).
  133. X. Turkeshi, L. Piroli, and M. Schirò, Density and current statistics in boundary-driven monitored fermionic chains, Phys. Rev. B 109, 144306 (2024).
  134. S. Roy, J. T. Chalker, I. V. Gornyi, and Y. Gefen, Measurement-induced steering of quantum systems, Phys. Rev. Res. 2, 033347 (2020).
  135. Y. Herasymenko, I. Gornyi, and Y. Gefen, Measurement-driven navigation in many-body Hilbert space: Active-decision steering, PRX Quantum 4, 020347 (2023).
  136. P. Pöpperl, I. V. Gornyi, and Y. Gefen, Measurements on an Anderson chain, Phys. Rev. B 107, 174203 (2023).
  137. S. Morales, Y. Gefen, I. Gornyi, A. Zazunov, and R. Egger, Engineering unsteerable quantum states with active feedback, Phys. Rev. Res. 6, 013244 (2024).
  138. X. Turkeshi, A. Biella, R. Fazio, M. Dalmonte, and M. Schiró, Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks, Phys. Rev. B 103, 224210 (2021).
  139. I. Poboiko, P. Pöpperl, I. V. Gornyi, and A. D. Mirlin, Measurement-induced transitions for interacting fermions, Phys. Rev. B 111, 024204 (2025).
  140. H. Guo, M. S. Foster, C.-M. Jian, and A. W. W. Ludwig, Field theory of monitored interacting fermion dynamics with charge conservation, Phys. Rev. B 112, 064304 (2025).
  141. U. Agrawal, A. Zabalo, K. Chen, J. H. Wilson, A. C. Potter, J. H. Pixley, S. Gopalakrishnan, and R. Vasseur, Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits, Phys. Rev. X 12, 041002 (2022).
  142. F. Barratt, U. Agrawal, S. Gopalakrishnan, D. A. Huse, R. Vasseur, and A. C. Potter, Field theory of charge sharpening in symmetric monitored quantum circuits, Phys. Rev. Lett. 129, 120604 (2022).
  143. F. Barratt, U. Agrawal, A. C. Potter, S. Gopalakrishnan, and R. Vasseur, Transitions in the learnability of global charges from local measurements, Phys. Rev. Lett. 129, 200602 (2022).
  144. M. Fisher, V. Khemani, A. Nahum, and S. Vijay, Random quantum circuits, Annu. Rev. Condens. Matter Phys. 14, 335 (2023).
  145. A. Nava, C. Artiaco, Y. Gefen, I. Gornyi, M. Tsitsishvili, A. Zazunov, and R. Egger, Dataset: Information transport and transport-induced entanglement in open fermion chains, Zenodo, 2026, http://doi.org/10.5281/zenodo.18199554.
  146. D. Gioev and I. Klich, Entanglement entropy of fermions in any dimension and the Widom conjecture, Phys. Rev. Lett. 96, 100503 (2006).
  147. G. Piccitto, A. Russomanno, and D. Rossini, Entanglement transitions in the quantum Ising chain: A comparison between different unravelings of the same Lindbladian, Phys. Rev. B 105, 064305 (2022).
  148. K. Mølmer, Y. Castin, and J. Dalibard, Monte Carlo wave-function method in quantum optics, J. Opt. Soc. Am. B 10, 524 (1993).
  149. N. Lambert, E. Giguère, P. Menczel, B. Li, P. Hopf, G. Su'arez, M. Gali, J. Lishman, R. Gadhvi, R. Agarwal, A. Galicia, N. Shammah, P. Nation, J. R. Johansson, S. Ahmed, S. Cross, A. Pitchford, and F. Nori, QuTiP 5: The quantum toolbox in Python, Phys. Rep. 1153, 1 (2026).

Outline

Information

Phys. Rev. Research 8, 033273– Published 3 September, 2026
  • Received 20 January 2026
  • Accepted 18 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation