Quantum Chaos and Coherence: Random Parametric Quantum Channels

Apollonas S. Matsoukas-Roubeas; Tomaž Prosen; Adolfo del Campo

doi:10.22331/q-2024-08-27-1446

Quantum Chaos and Coherence: Random Parametric Quantum Channels

Apollonas S. Matsoukas-Roubeas¹, Tomaž Prosen², and Adolfo del Campo^1,3

¹Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, G. D. Luxembourg
²Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
³Donostia International Physics Center, E-20018 San Sebastián, Spain

Published:	2024-08-27, volume 8, page 1446
Eprint:	arXiv:2305.19326v3
Doi:	https://doi.org/10.22331/q-2024-08-27-1446
Citation:	Quantum 8, 1446 (2024).

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Abstract

The survival probability of an initial Coherent Gibbs State (CGS) is a natural extension of the Spectral Form Factor (SFF) to open quantum systems. To quantify the interplay between quantum chaos and decoherence away from the semi-classical limit, we investigate the relation of this generalized SFF with the corresponding $l_1$-norm of coherence. As a working example, we introduce Parametric Quantum Channels (PQC), a discrete-time model of unitary evolution mixed with the effects of measurements or transient interactions with an environment. The Energy Dephasing (ED) dynamics arises as a specific case in the Markovian limit. We demonstrate our results in a series of random matrix models.

► BibTeX data

@article{MatsoukasRoubeas2024quantumchaos,
  doi = {10.22331/q-2024-08-27-1446},
  url = {https://doi.org/10.22331/q-2024-08-27-1446},
  title = {Quantum {C}haos and {C}oherence: {R}andom {P}arametric {Q}uantum {C}hannels},
  author = {Matsoukas-Roubeas, Apollonas S. and Prosen, Toma{\v{z}} and Campo, Adolfo del},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1446},
  month = aug,
  year = {2024}
}

► References

[1] Martin C. Gutzwiller. ``Chaos in Classical and Quantum Mechanics''. Springer. New York (1990).
https://doi.org/10.1007/978-1-4612-0983-6

[2] Fritz Haake, Sven Gnutzmann, and Marek Kuś. ``Quantum Signatures of Chaos''. Springer International Publishing. Cham (2018).
https://doi.org/10.1007/978-3-319-97580-1_5

[3] Heinz-Peter Breuer and Francesco Petruccione. ``The Theory of Open Quantum Systems''. Oxford University Press. (2007).

[4] Angel Rivas and Susana F. Huelga. ``Open quantum systems: An introduction''. Springer. Berlin, Heidelberg (2012).
https://doi.org/10.1007/978-3-642-23354-8_4

[5] Daniel Braun. ``Dissipative quantum chaos and decoherence''. Springer Berlin, Heidelberg. (2001).
https://doi.org/10.1007/3-540-40916-5

[6] Wojciech Hubert Zurek and Juan Pablo Paz. ``Decoherence, chaos, and the second law''. Phys. Rev. Lett. 72, 2508–2511 (1994).
https://doi.org/10.1103/PhysRevLett.72.2508

[7] Zbyszek P. Karkuszewski, Christopher Jarzynski, and Wojciech H. Zurek. ``Quantum chaotic environments, the butterfly effect, and decoherence''. Phys. Rev. Lett. 89, 170405 (2002).
https://doi.org/10.1103/PhysRevLett.89.170405

[8] Wojciech Hubert Zurek. ``Decoherence, einselection, and the quantum origins of the classical''. Rev. Mod. Phys. 75, 715–775 (2003).
https://doi.org/10.1103/RevModPhys.75.715

[9] Salman Habib, Tanmoy Bhattacharya, Benjamin Greenbaum, Kurt Jacobs, Kosuke Shizume, and Bala Sundaram. ``Chaos and Quantum Mechanics''. Ann. N. Y. Acad. Sci. 1045, 308–332 (2005).
https://doi.org/10.1196/annals.1350.026

[10] Michael Victor Berry, M. Tabor, and John Michael Ziman. ``Level clustering in the regular spectrum''. Proc. R. Soc. Lond. A 356, 375–394 (1977).
https://doi.org/10.1098/rspa.1977.0140

[11] O. Bohigas, M. J. Giannoni, and C. Schmit. ``Characterization of chaotic quantum spectra and universality of level fluctuation laws''. Phys. Rev. Lett. 52, 1–4 (1984).
https://doi.org/10.1103/PhysRevLett.52.1

[12] Luc Leviandier, Maurice Lombardi, Rémi Jost, and Jean Paul Pique. ``Fourier transform: A tool to measure statistical level properties in very complex spectra''. Phys. Rev. Lett. 56, 2449–2452 (1986).
https://doi.org/10.1103/PhysRevLett.56.2449

[13] Joshua Wilkie and Paul Brumer. ``Time-dependent manifestations of quantum chaos''. Phys. Rev. Lett. 67, 1185–1188 (1991).
https://doi.org/10.1103/PhysRevLett.67.1185

[14] Y. Alhassid and R. D. Levine. ``Spectral autocorrelation function in the statistical theory of energy levels''. Phys. Rev. A 46, 4650–4653 (1992).
https://doi.org/10.1103/PhysRevA.46.4650

[15] Jian-Zhong Ma. ``Correlation Hole of Survival Probability and Level Statistics''. J. Phys. Soc. Jpn. 64, 4059–4063 (1995).
https://doi.org/10.1143/JPSJ.64.4059

[16] Thomas Gorin, Tomaz Prosen, Thomas H. Seligman, and Marko Žnidarič. ``Dynamics of Loschmidt echoes and fidelity decay''. Phys. Rep. 435, 33–156 (2006).
https://doi.org/10.1016/j.physrep.2006.09.003

[17] Aurélia Chenu, Javier Molina-Vilaplana, and Adolfo del Campo. ``Work statistics, loschmidt echo and information scrambling in chaotic quantum systems''. Quantum 3, 127 (2019).
https://doi.org/10.22331/q-2019-03-04-127

[18] Benoît Collins and Ion Nechita. ``Random Quantum Channels I: Graphical Calculus and the Bell State Phenomenon''. Commun. Math. Phys. 297, 345–370 (2010).
https://doi.org/10.1007/s00220-010-1012-0

[19] Benoît Collins and Ion Nechita. ``Random matrix techniques in quantum information theory''. J. Math. Phys. 57, 015215 (2015).
https://doi.org/10.1063/1.4936880

[20] Jordan S. Cotler, Guy Gur-Ari, Masanori Hanada, Joseph Polchinski, Phil Saad, Stephen H. Shenker, Douglas Stanford, Alexandre Streicher, and Masaki Tezuka. ``Black holes and random matrices''. JHEP 2017, 118 (2017).
https://doi.org/10.1007/JHEP05(2017)118

[21] Adolfo del Campo and Tadashi Takayanagi. ``Decoherence in Conformal Field Theory''. JHEP 2020, 170 (2020).
https://doi.org/10.1007/JHEP02(2020)170

[22] Zhenyu Xu, Luis Pedro García-Pintos, Aurélia Chenu, and Adolfo del Campo. ``Extreme decoherence and quantum chaos''. Phys. Rev. Lett. 122, 014103 (2019).
https://doi.org/10.1103/PhysRevLett.122.014103

[23] Zan Cao, Zhenyu Xu, and Adolfo del Campo. ``Probing quantum chaos in multipartite systems''. Phys. Rev. Res. 4, 033093 (2022).
https://doi.org/10.1103/PhysRevResearch.4.033093

[24] Xiaoguang Wang, Shohini Ghose, Barry C. Sanders, and Bambi Hu. ``Entanglement as a signature of quantum chaos''. Phys. Rev. E 70, 016217 (2004).
https://doi.org/10.1103/PhysRevE.70.016217

[25] Tomaz Prosen and Iztok Pižorn. ``Operator space entanglement entropy in a transverse ising chain''. Phys. Rev. A 76, 032316 (2007).
https://doi.org/10.1103/PhysRevA.76.032316

[26] S. Chaudhury, A. Smith, B. E. Anderson, S. Ghose, and P. S. Jessen. ``Quantum signatures of chaos in a kicked top''. Nature 461, 768–771 (2009).
https://doi.org/10.1038/nature08396

[27] C. Neill, P. Roushan, M. Fang, Y. Chen, M. Kolodrubetz, Z. Chen, A. Megrant, R. Barends, B. Campbell, B. Chiaro, et al. ``Ergodic dynamics and thermalization in an isolated quantum system''. Nat. Phys. 12, 1037–1041 (2016).
https://doi.org/10.1038/nphys3830

[28] Lev Vidmar and Marcos Rigol. ``Entanglement entropy of eigenstates of quantum chaotic hamiltonians''. Phys. Rev. Lett. 119, 220603 (2017).
https://doi.org/10.1103/PhysRevLett.119.220603

[29] E. J. Torres-Herrera and Lea F. Santos. ``Dynamical manifestations of quantum chaos: correlation hole and bulge''. Phil. Trans. R. Soc. A. 375, 20160434 (2017).
https://doi.org/10.1098/rsta.2016.0434

[30] Meenu Kumari and Shohini Ghose. ``Untangling entanglement and chaos''. Phys. Rev. A 99, 042311 (2019).
https://doi.org/10.1103/PhysRevA.99.042311

[31] Neil Dowling and Kavan Modi. ``Operational metric for quantum chaos and the corresponding spatiotemporal-entanglement structure''. PRX Quantum 5, 010314 (2024).
https://doi.org/10.1103/PRXQuantum.5.010314

[32] Vaibhav Madhok, Vibhu Gupta, Denis-Alexandre Trottier, and Shohini Ghose. ``Signatures of chaos in the dynamics of quantum discord''. Phys. Rev. E 91, 032906 (2015).
https://doi.org/10.1103/PhysRevE.91.032906

[33] Martin Sieber and Klaus Richter. ``Correlations between periodic orbits and their rôle in spectral statistics''. Phys. Scr. 2001, 128 (2001).
https://doi.org/10.1238/Physica.Topical.090a00128

[34] Piotr Sierant, Artur Maksymov, Marek Kuś, and Jakub Zakrzewski. ``Fidelity susceptibility in gaussian random ensembles''. Phys. Rev. E 99, 050102 (2019).
https://doi.org/10.1103/PhysRevE.99.050102

[35] Dries Sels and Anatoli Polkovnikov. ``Dynamical obstruction to localization in a disordered spin chain''. Phys. Rev. E 104, 054105 (2021).
https://doi.org/10.1103/PhysRevE.104.054105

[36] A. I. Larkin and Yu N Ovchinnikov. ``Quasiclassical Method in the Theory of Superconductivity''. Soviet Physics JETP 28, 1200 (1969). url: http://jetp.ras.ru/cgi-bin/dn/e_028_06_1200.pdf.
http://jetp.ras.ru/cgi-bin/dn/e_028_06_1200.pdf

[37] Koji Hashimoto, Keiju Murata, and Ryosuke Yoshii. ``Out-of-time-order correlators in quantum mechanics''. JHEP 2017, 138 (2017).
https://doi.org/10.1007/JHEP10(2017)138

[38] Juan Maldacena, Stephen H. Shenker, and Douglas Stanford. ``A bound on chaos''. JHEP 2016, 106 (2016).
https://doi.org/10.1007/JHEP08(2016)106

[39] J. M. Deutsch. ``Quantum statistical mechanics in a closed system''. Phys. Rev. A 43, 2046–2049 (1991).
https://doi.org/10.1103/PhysRevA.43.2046

[40] Mark Srednicki. ``Chaos and quantum thermalization''. Phys. Rev. E 50, 888–901 (1994).
https://doi.org/10.1103/PhysRevE.50.888

[41] Marcos Rigol, Vanja Dunjko, and Maxim Olshanii. ``Thermalization and its mechanism for generic isolated quantum systems''. Nature 452, 854–858 (2008).
https://doi.org/10.1038/nature06838

[42] Luca D'Alessio, Yariv Kafri, Anatoli Polkovnikov, and Marcos Rigol. ``From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics''. Adv. Phys. 65, 239–362 (2016).
https://doi.org/10.1080/00018732.2016.1198134

[43] A Bohrdt, C B Mendl, M Endres, and M Knap. ``Scrambling and thermalization in a diffusive quantum many-body system''. New J. Phys. 19, 063001 (2017).
https://doi.org/10.1088/1367-2630/aa719b

[44] Chaitanya Murthy and Mark Srednicki. ``Bounds on chaos from the eigenstate thermalization hypothesis''. Phys. Rev. Lett. 123, 230606 (2019).
https://doi.org/10.1103/PhysRevLett.123.230606

[45] Patrick Hayden and John Preskill. ``Black holes as mirrors: quantum information in random subsystems''. JHEP 2007, 120 (2007).
https://doi.org/10.1088/1126-6708/2007/09/120

[46] Yasuhiro Sekino and L. Susskind. ``Fast scramblers''. JHEP 2008, 065 (2008).
https://doi.org/10.1088/1126-6708/2008/10/065

[47] Daniel A. Roberts and Beni Yoshida. ``Chaos and complexity by design''. JHEP 2017, 121 (2017).
https://doi.org/10.1007/JHEP04(2017)121

[48] Xiao Mi, Pedram Roushan, Chris Quintana, Salvatore Mandrà, Jeffrey Marshall, Charles Neill, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, et al. ``Information scrambling in quantum circuits''. Science 374, 1479–1483 (2021).
https://doi.org/10.1126/science.abg5029

[49] Adam Nahum, Sagar Vijay, and Jeongwan Haah. ``Operator spreading in random unitary circuits''. Phys. Rev. X 8, 021014 (2018).
https://doi.org/10.1103/PhysRevX.8.021014

[50] C. W. von Keyserlingk, Tibor Rakovszky, Frank Pollmann, and S. L. Sondhi. ``Operator hydrodynamics, otocs, and entanglement growth in systems without conservation laws''. Phys. Rev. X 8, 021013 (2018).
https://doi.org/10.1103/PhysRevX.8.021013

[51] Israel Reichental, Anat Klempner, Yariv Kafri, and Daniel Podolsky. ``Thermalization in open quantum systems''. Phys. Rev. B 97, 134301 (2018).
https://doi.org/10.1103/PhysRevB.97.134301

[52] Paolo Zanardi and Namit Anand. ``Information scrambling and chaos in open quantum systems''. Phys. Rev. A 103, 062214 (2021).
https://doi.org/10.1103/PhysRevA.103.062214

[53] Thomas Schuster and Norman Y. Yao. ``Operator growth in open quantum systems''. Phys. Rev. Lett. 131, 160402 (2023).
https://doi.org/10.1103/PhysRevLett.131.160402

[54] Arpan Bhattacharyya, Wissam Chemissany, S. Shajidul Haque, and Bin Yan. ``Towards the web of quantum chaos diagnostics''. The European Physical Journal C 82 (2022).
https://doi.org/10.1140/epjc/s10052-022-10035-3

[55] Gernot Akemann, Mario Kieburg, Adam Mielke, and Tomaz Prosen. ``Universal signature from integrability to chaos in dissipative open quantum systems''. Phys. Rev. Lett. 123, 254101 (2019).
https://doi.org/10.1103/PhysRevLett.123.254101

[56] Tomaž Prosen and Marko Žnidarič. ``Eigenvalue statistics as an indicator of integrability of nonequilibrium density operators''. Phys. Rev. Lett. 111, 124101 (2013).
https://doi.org/10.1103/PhysRevLett.111.124101

[57] Pedro Ribeiro and Tomaz Prosen. ``Integrable quantum dynamics of open collective spin models''. Phys. Rev. Lett. 122, 010401 (2019).
https://doi.org/10.1103/PhysRevLett.122.010401

[58] Lucas Sá, Pedro Ribeiro, Tankut Can, and Tomaz Prosen. ``Spectral transitions and universal steady states in random kraus maps and circuits''. Phys. Rev. B 102, 134310 (2020).
https://doi.org/10.1103/PhysRevB.102.134310

[59] Lucas Sá, Pedro Ribeiro, and Tomaz Prosen. ``Spectral and steady-state properties of random Liouvillians''. J. Phys. A: Math. Theor. 53, 305303 (2020).
https://doi.org/10.1088/1751-8121/ab9337

[60] Lucas Sá, Pedro Ribeiro, and Tomaz Prosen. ``Complex spacing ratios: A signature of dissipative quantum chaos''. Phys. Rev. X 10, 021019 (2020).
https://doi.org/10.1103/PhysRevX.10.021019

[61] Yuto Ashida, Zongping Gong, and Masahito Ueda. ``Non-hermitian physics''. Adv. Phys. 69, 249–435 (2020).
https://doi.org/10.1080/00018732.2021.1876991

[62] Ryusuke Hamazaki, Kohei Kawabata, Naoto Kura, and Masahito Ueda. ``Universality classes of non-hermitian random matrices''. Phys. Rev. Research 2, 023286 (2020).
https://doi.org/10.1103/PhysRevResearch.2.023286

[63] Antonio M. García-García, Lucas Sá, and Jacobus J. M. Verbaarschot. ``Symmetry classification and universality in non-hermitian many-body quantum chaos by the sachdev-ye-kitaev model''. Phys. Rev. X 12, 021040 (2022).
https://doi.org/10.1103/PhysRevX.12.021040

[64] Lucas Sá, Pedro Ribeiro, and TomažProsen. ``Symmetry classification of many-body lindbladians: Tenfold way and beyond''. Phys. Rev. X 13, 031019 (2023).
https://doi.org/10.1103/PhysRevX.13.031019

[65] Kohei Kawabata, Anish Kulkarni, Jiachen Li, Tokiro Numasawa, and Shinsei Ryu. ``Symmetry of open quantum systems: Classification of dissipative quantum chaos''. PRX Quantum 4, 030328 (2023).
https://doi.org/10.1103/PRXQuantum.4.030328

[66] A. Uhlmann. ``The “transition probability” in the state space of a $*$-algebra''. Rep. Math. Phys. 9, 273–279 (1976).
https://doi.org/10.1016/0034-4877(76)90060-4

[67] A. del Campo, J. Molina-Vilaplana, and J. Sonner. ``Scrambling the spectral form factor: Unitarity constraints and exact results''. Phys. Rev. D 95, 126008 (2017).
https://doi.org/10.1103/PhysRevD.95.126008

[68] Zhenyu Xu, Aurelia Chenu, Tomaz Prosen, and Adolfo del Campo. ``Thermofield dynamics: Quantum chaos versus decoherence''. Phys. Rev. B 103, 064309 (2021).
https://doi.org/10.1103/PhysRevB.103.064309

[69] Julien Cornelius, Zhenyu Xu, Avadh Saxena, Aurélia Chenu, and Adolfo del Campo. ``Spectral filtering induced by non-hermitian evolution with balanced gain and loss: Enhancing quantum chaos''. Phys. Rev. Lett. 128, 190402 (2022).
https://doi.org/10.1103/PhysRevLett.128.190402

[70] Apollonas S. Matsoukas-Roubeas, Federico Roccati, Julien Cornelius, Zhenyu Xu, Aurélia Chenu, and Adolfo del Campo. ``Non-Hermitian Hamiltonian deformations in quantum mechanics''. JHEP 2023, 60 (2023).
https://doi.org/10.1007/JHEP01(2023)060

[71] Jiachen Li, Tomaz Prosen, and Amos Chan. ``Spectral statistics of non-hermitian matrices and dissipative quantum chaos''. Phys. Rev. Lett. 127, 170602 (2021).
https://doi.org/10.1103/PhysRevLett.127.170602

[72] Amit Vikram and Victor Galitski. ``Exact universal bounds on quantum dynamics and fast scrambling''. Phys. Rev. Lett. 132, 040402 (2024).
https://doi.org/10.1103/PhysRevLett.132.040402

[73] Yi-Neng Zhou, Tian-Gang Zhou, and Pengfei Zhang. ``Universal properties of the spectral form factor in open quantum systems'' (2023). arXiv:2303.14352.
https://doi.org/10.1007/s11467-024-1406-7
arXiv:2303.14352

[74] Yunxiang Liao and Victor Galitski. ``Universal dephasing mechanism of many-body quantum chaos''. Phys. Rev. Research 4, L012037 (2022).
https://doi.org/10.1103/PhysRevResearch.4.L012037

[75] Alexander Streltsov, Gerardo Adesso, and Martin B. Plenio. ``Colloquium: Quantum coherence as a resource''. Rev. Mod. Phys. 89, 041003 (2017).
https://doi.org/10.1103/RevModPhys.89.041003

[76] Paolo Zanardi, Georgios Styliaris, and Lorenzo Campos Venuti. ``Coherence-generating power of quantum unitary maps and beyond''. Phys. Rev. A 95, 052306 (2017).
https://doi.org/10.1103/PhysRevA.95.052306

[77] Georgios Styliaris, Lorenzo Campos Venuti, and Paolo Zanardi. ``Coherence-generating power of quantum dephasing processes''. Phys. Rev. A 97, 032304 (2018).
https://doi.org/10.1103/PhysRevA.97.032304

[78] Georgios Styliaris, Namit Anand, Lorenzo Campos Venuti, and Paolo Zanardi. ``Quantum coherence and the localization transition''. Phys. Rev. B 100, 224204 (2019).
https://doi.org/10.1103/PhysRevB.100.224204

[79] Namit Anand, Georgios Styliaris, Meenu Kumari, and Paolo Zanardi. ``Quantum coherence as a signature of chaos''. Phys. Rev. Research 3, 023214 (2021).
https://doi.org/10.1103/PhysRevResearch.3.023214

[80] Alexander Streltsov, Hermann Kampermann, Sabine Wölk, Manuel Gessner, and Dagmar Bruß. ``Maximal coherence and the resource theory of purity''. New J. Phys. 20, 053058 (2018).
https://doi.org/10.1088/1367-2630/aac484

[81] Eric Chitambar and Gilad Gour. ``Quantum resource theories''. Rev. Mod. Phys. 91, 025001 (2019).
https://doi.org/10.1103/RevModPhys.91.025001

[82] Andreas Winter and Dong Yang. ``Operational resource theory of coherence''. Phys. Rev. Lett. 116, 120404 (2016).
https://doi.org/10.1103/PhysRevLett.116.120404

[83] Michael M. Wolf and J. Ignacio Cirac. ``Dividing Quantum Channels''. Commun. Math. Phys. 279, 147–168 (2008).
https://doi.org/10.1007/s00220-008-0411-y

[84] Ángel Rivas, Susana F Huelga, and Martin B Plenio. ``Quantum non-markovianity: characterization, quantification and detection''. Rep. Prog. Phys. 77, 094001 (2014).
https://doi.org/10.1088/0034-4885/77/9/094001

[85] T. Guhr and H. A. Weidenmuller. ``Correlations in anticrossing spectra and scattering theory. Analytical aspects''. Chem. Phys. 146, 21–38 (1990).
https://doi.org/10.1016/0301-0104(90)90003-R

[86] Pablo Martinez-Azcona and Aurélia Chenu. ``Analyticity constraints bound the decay of the spectral form factor''. Quantum 6, 852 (2022).
https://doi.org/10.22331/q-2022-11-03-852

[87] Jerryman A. Gyamfi. ``Fundamentals of quantum mechanics in Liouville space''. Eur. J. Phys. 41, 063002 (2020).
https://doi.org/10.1088/1361-6404/ab9fdd

[88] T. Baumgratz, M. Cramer, and M. B. Plenio. ``Quantifying coherence''. Phys. Rev. Lett. 113, 140401 (2014).
https://doi.org/10.1103/PhysRevLett.113.140401

[89] Federico Levi and Florian Mintert. ``A quantitative theory of coherent delocalization''. New J. Phys. 16, 033007 (2014).
https://doi.org/10.1088/1367-2630/16/3/033007

[90] I. L. Egusquiza, L. J. Garay, and J. M. Raya. ``Quantum evolution according to real clocks''. Phys. Rev. A 59, 3236–3240 (1999).
https://doi.org/10.1103/PhysRevA.59.3236

[91] Stephen L. Adler. ``Weisskopf-wigner decay theory for the energy-driven stochastic schrödinger equation''. Phys. Rev. D 67, 025007 (2003).
https://doi.org/10.1103/PhysRevD.67.025007

[92] N. Gisin. ``Quantum measurements and stochastic processes''. Phys. Rev. Lett. 52, 1657–1660 (1984).
https://doi.org/10.1103/PhysRevLett.52.1657

[93] G. J. Milburn. ``Intrinsic decoherence in quantum mechanics''. Phys. Rev. A 44, 5401–5406 (1991).
https://doi.org/10.1103/PhysRevA.44.5401

[94] I. C. Percival. ``Primary state diffusion''. Proc. R. Soc. A. 447, 189–209 (1994).
https://doi.org/10.1098/rspa.1994.0135

[95] Angelo Bassi, Kinjalk Lochan, Seema Satin, Tejinder P. Singh, and Hendrik Ulbricht. ``Models of wave-function collapse, underlying theories, and experimental tests''. Rev. Mod. Phys. 85, 471–527 (2013).
https://doi.org/10.1103/RevModPhys.85.471

[96] Mauro Schiulaz, E. Jonathan Torres-Herrera, and Lea F. Santos. ``Thouless and relaxation time scales in many-body quantum systems''. Phys. Rev. B 99, 174313 (2019).
https://doi.org/10.1103/PhysRevB.99.174313

[97] J.L.F. Barbón and E. Rabinovici. ``Geometry and quantum noise''. Fortschr. Phys. 62, 626–646 (2014).
https://doi.org/10.1002/prop.201400044

[98] Piotr Sierant, Giuliano Chiriacò, Federica M. Surace, Shraddha Sharma, Xhek Turkeshi, Marcello Dalmonte, Rosario Fazio, and Guido Pagano. ``Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains''. Quantum 6, 638 (2022).
https://doi.org/10.22331/q-2022-02-02-638

[99] K. Kraus. ``States, Effects, and Operations: Fundamental Notions of Quantum Theory''. Lecture Notes in Physics. Springer-Verlag. Berlin Heidelberg (1983).
https://doi.org/10.1007/3-540-12732-1

[100] G. Lindblad. ``On the generators of quantum dynamical semigroups''. Commun. Math. Phys. 48, 119–130 (1976).
https://doi.org/10.1007/BF01608499

[101] Vittorio Gorini, Andrzej Kossakowski, and E. C. G. Sudarshan. ``Completely positive dynamical semigroups of N‐level systems''. J. Math. Phys. 17, 821–825 (1976).
https://doi.org/10.1063/1.522979

[102] M. M. Wolf, J. Eisert, T. S. Cubitt, and J. I. Cirac. ``Assessing non-markovian quantum dynamics''. Phys. Rev. Lett. 101, 150402 (2008).
https://doi.org/10.1103/PhysRevLett.101.150402

[103] Felix A. Pollock, César Rodríguez-Rosario, Thomas Frauenheim, Mauro Paternostro, and Kavan Modi. ``Operational markov condition for quantum processes''. Phys. Rev. Lett. 120, 040405 (2018).
https://doi.org/10.1103/PhysRevLett.120.040405

[104] Simon Milz, M. S. Kim, Felix A. Pollock, and Kavan Modi. ``Completely positive divisibility does not mean markovianity''. Phys. Rev. Lett. 123, 040401 (2019).
https://doi.org/10.1103/PhysRevLett.123.040401

[105] M. L. Mehta. ``Random matrices, 3rd ed.''. Elsevier. San Diego (2004). url: https://www.elsevier.com/books/random-matrices/lal-mehta/978-0-12-088409-4.
https://www.elsevier.com/books/random-matrices/lal-mehta/978-0-12-088409-4

[106] Karol Zyczkowski and Hans-Jürgen Sommers. ``Truncations of random unitary matrices''. J. Phys. A: Math. Gen. 33, 2045 (2000).
https://doi.org/10.1088/0305-4470/33/10/307

[107] Wojciech Bruzda, Marek Smaczyński, Valerio Cappellini, Hans-Jürgen Sommers, and Karol Życzkowski. ``Universality of spectra for interacting quantum chaotic systems''. Phys. Rev. E 81, 066209 (2010).
https://doi.org/10.1103/PhysRevE.81.066209

[108] Wojciech Bruzda, Valerio Cappellini, Hans-Jürgen Sommers, and Karol Życzkowski. ``Random quantum operations''. Phys. Lett. A 373, 320–324 (2009).
https://doi.org/10.1016/j.physleta.2008.11.043

[109] Ryszard Kukulski, Ion Nechita, Łukasz Pawela, Zbigniew Puchała, and Karol Życzkowski. ``Generating random quantum channels''. J. Math. Phys. 62, 062201 (2021).
https://doi.org/10.1063/5.0038838

[110] Joshua Feinberg and A. Zee. ``Non-hermitian random matrix theory: Method of hermitian reduction''. Nucl. Phys. B 504, 579–608 (1997).
https://doi.org/10.1016/S0550-3213(97)00502-6

[111] C. Wang and X. R. Wang. ``Level statistics of extended states in random non-Hermitian Hamiltonians''. Phys. Rev. B 101, 165114 (2020).
https://doi.org/10.1103/PhysRevB.101.165114

[112] Ken Mochizuki, Naomichi Hatano, Joshua Feinberg, and Hideaki Obuse. ``Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms''. Phys. Rev. E 102, 012101 (2020).
https://doi.org/10.1103/PhysRevE.102.012101

[113] G. Marinello and M. P. Pato. ``Random non-hermitian tight-binding models''. J. Phys.: Conf. Ser. 738, 012040 (2016).
https://doi.org/10.1088/1742-6596/738/1/012040

[114] Kevin Wang, Francesco Piazza, and David J. Luitz. ``Hierarchy of Relaxation Timescales in Local Random Liouvillians''. Phys. Rev. Lett. 124, 100604 (2020).
https://doi.org/10.1103/PhysRevLett.124.100604

[115] Sergey Denisov, Tetyana Laptyeva, Wojciech Tarnowski, Dariusz Chruściński, and Karol Życzkowski. ``Universal spectra of random lindblad operators''. Phys. Rev. Lett. 123, 140403 (2019).
https://doi.org/10.1103/PhysRevLett.123.140403

[116] Tankut Can. ``Random lindblad dynamics''. J. Phys. A: Math. Theor. 52, 485302 (2019).
https://doi.org/10.1088/1751-8121/ab4d26

[117] Tankut Can, Vadim Oganesyan, Dror Orgad, and Sarang Gopalakrishnan. ``Spectral gaps and midgap states in random quantum master equations''. Phys. Rev. Lett. 123, 234103 (2019).
https://doi.org/10.1103/PhysRevLett.123.234103

[118] Stefan Lange and Carsten Timm. ``Random-matrix theory for the Lindblad master equation''. Chaos 31, 023101 (2021).
https://doi.org/10.1063/5.0033486

[119] Jean Ginibre. ``Statistical Ensembles of Complex, Quaternion, and Real Matrices''. J. Math. Phys. 6, 440 (1965).
https://doi.org/10.1063/1.1704292

[120] V. L. Girko. ``Circular law''. Theory Probab. Appl 29, 694–706 (1985).
https://doi.org/10.1137/1129095

[121] Joshua Feinberg, R. Scalettar, and A. Zee. ``“Single ring theorem” and the disk-annulus phase transition''. J. Math. Phys. 42, 5718–5740 (2001).
https://doi.org/10.1063/1.1412599

[122] L G Molinari and G Lacagnina. ``Disk-annulus transition and localization in random non-hermitian tridiagonal matrices''. J. Phys. A: Math. Theor. 42, 395204 (2009).
https://doi.org/10.1088/1751-8113/42/39/395204

[123] Terence Tao and Van Vu. ``Random Matrices: Universality of ESDs and the Circular Law''. Ann. Probab. 38, 2023–2065 (2010). url: https://www.jstor.org/stable/25734717.
https://www.jstor.org/stable/25734717

[124] Friedrich Götze and Alexander Tikhomirov. ``The circular law for random matrices''. Ann. Probab. 38, 1444 – 1491 (2010).
https://doi.org/10.1214/09-AOP522

[125] Alice Guionnet, Manjunath Krishnapur, and Ofer Zeitouni. ``The single ring theorem''. Ann. Math. 174, 1189–1217 (2011). url: https://www.jstor.org/stable/23030522.
https://www.jstor.org/stable/23030522

[126] Jonit Fischmann, Wojciech Bruzda, Boris A. Khoruzhenko, Hans-Jürgen Sommers, and Karol Zyczkowski. ``Induced Ginibre ensemble of random matrices and quantum operations''. J. Phys. A: Math. Theor. 45, 075203 (2012).
https://doi.org/10.1088/1751-8113/45/7/075203

[127] John Preskill. ``Quantum Computing in the NISQ era and beyond''. Quantum 2, 79 (2018).
https://doi.org/10.22331/q-2018-08-06-79

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