Decoherence rate in random Lindblad dynamics

Chaotics; Classical behavior; Decoherence; Decoherence rates; Lindblad; Lindblad operators; Open quantum systems; Quantum system; Time-scales; Upper limits; Physics and Astronomy (all); Quantum Physics; Physics - Statistical Mechanics; High Energy Physics - Theory

Abstract :

[en] Open quantum systems undergo decoherence, which is responsible for the transition from quantum to classical behavior. The time scale in which decoherence takes place can be analyzed using upper limits to its rate. We examine the dynamics of open chaotic quantum systems governed by random Lindblad operators sourced from Gaussian and Ginibre ensembles with Wigner-Dyson symmetry classes. In these systems, the ensemble-averaged purity decays monotonically as a function of time. This decay is governed by the decoherence rate, which is upper-bounded by the dimension of their Hilbert space and is independent of the ensemble symmetry. These findings hold upon mixing different ensembles, indicating the universal character of the decoherence rate limit. Moreover, our findings reveal that open chaotic quantum systems governed by random Lindbladians tend to exhibit the most rapid decoherence, regardless of the initial state. This phenomenon is associated with the concentration of the decoherence rate near its upper bound. Our work identifies primary features of decoherence in dissipative quantum chaos, with applications ranging from quantum foundations to high-energy physics and quantum technologies.

Disciplines :

Physics

Author, co-author :

Yang, Yifeng ^✱; School of Physical Science and Technology, Soochow University, Suzhou, China

Xu, Zhenyu ^✱; School of Physical Science and Technology, Soochow University, Suzhou, China

DEL CAMPO ECHEVARRIA, Adolfo ^✱; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) ; Donostia International Physics Center

^✱ These authors have contributed equally to this work.

External co-authors :

yes

Language :

English

Title :

Decoherence rate in random Lindblad dynamics

Publication date :

03 June 2024

Journal title :

Physical Review Research

eISSN :

2643-1564

Publisher :

American Physical Society

Volume :

Issue :

Peer reviewed :

Editorial reviewed

Additional URL :

https://link.aps.org/article/10.1103/PhysRevResearch.6.023229

Funders :

National Natural Science Foundation of China
Fonds National de la Recherche Luxembourg

Funding text :

The authors are indebted to Lucas S\u00E1, Federico Balducci, and Pablo Azcona for insightful comments on the manuscript. This work was supported by the National Natural Science Foundation of China under Grant No.12074280 and by the Luxembourg National Research Fund (FNR), Grant No. 17132054.

Commentary :

13 pages, 6 figures

Available on ORBilu :

since 11 September 2024

Statistics

Number of views

80 (1 by Unilu)

Number of downloads

45 (0 by Unilu)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

WoS citations^™

Bibliography

W. H. Zurek, Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse Phys. Rev. D 24, 1516 (1981) 0556-2821 10.1103/PhysRevD.24.1516.
W. H. Zurek, Environment-induced superselection rules, Phys. Rev. D 26, 1862 (1982) 0556-2821 10.1103/PhysRevD.26.1862.
W. H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Rev. Mod. Phys. 75, 715 (2003) 0034-6861 10.1103/RevModPhys.75.715.
M. Schlosshauer, Quantum decoherence, Phys. Rep. 831, 1 (2019) 0370-1573 10.1016/j.physrep.2019.10.001.
M. Schlosshauer, Decoherence and the Quantum-To-Classical Transition (Springer, Berlin, 2007).
W. H. Zurek, Decoherence and the transition from quantum to classical, Phys. Today 44(10), 36 (1991) 0031-9228 10.1063/1.881293.
W. H. Zurek, S. Habib, and J. P. Paz, Coherent states via decoherence, Phys. Rev. Lett. 70, 1187 (1993) 0031-9007 10.1103/PhysRevLett.70.1187.
W. H. Zurek and J. P. Paz, Decoherence, chaos, and the second law, Phys. Rev. Lett. 72, 2508 (1994) 0031-9007 10.1103/PhysRevLett.72.2508.
V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of (Equation presented)-level systems, J. Math. Phys. 17, 821 (1976) 0022-2488 10.1063/1.522979.
G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976) 0010-3616 10.1007/BF01608499.
D. A. Lidar, I. L. Chuang, and K. B. Whaley, Decoherence-free subspaces for quantum computation, Phys. Rev. Lett. 81, 2594 (1998) 0031-9007 10.1103/PhysRevLett.81.2594.
A. Shimizu and T. Miyadera, Stability of quantum states of finite macroscopic systems against classical noises, perturbations from environments, and local measurements, Phys. Rev. Lett. 89, 270403 (2002) 0031-9007 10.1103/PhysRevLett.89.270403.
A. Chenu, M. Beau, J. Cao, and A. del Campo, Quantum simulation of generic many-body open system dynamics using classical noise, Phys. Rev. Lett. 118, 140403 (2017) 0031-9007 10.1103/PhysRevLett.118.140403.
M. Beau, J. Kiukas, I. L. Egusquiza, and A. del Campo, Nonexponential quantum decay under environmental decoherence, Phys. Rev. Lett. 119, 130401 (2017) 0031-9007 10.1103/PhysRevLett.119.130401.
Z. Xu, L. P. García-Pintos, A. Chenu, and A. del Campo, Extreme decoherence and quantum chaos, Phys. Rev. Lett. 122, 014103 (2019) 0031-9007 10.1103/PhysRevLett.122.014103.
Z. Xu, A. Chenu, T. Prosen, and A. del Campo, Thermofield dynamics: Quantum chaos versus decoherence, Phys. Rev. B 103, 064309 (2021) 2469-9950 10.1103/PhysRevB.103.064309.
L. P. García-Pintos and A. del Campo, Limits to perception by quantum monitoring with finite efficiency, Entropy 23, 1527 (2021) 1099-4300 10.3390/e23111527.
M. Kiciński and J. K. Korbicz, Decoherence and objectivity in higher spin environments, Phys. Rev. A 104, 042216 (2021) 2469-9926 10.1103/PhysRevA.104.042216.
S. Habib, K. Shizume, and W. H. Zurek, Decoherence, chaos, and the correspondence principle, Phys. Rev. Lett. 80, 4361 (1998) 0031-9007 10.1103/PhysRevLett.80.4361.
Z. P. Karkuszewski, C. Jarzynski, and W. H. Zurek, Quantum chaotic environments, the butterfly effect, and decoherence, Phys. Rev. Lett. 89, 170405 (2002) 0031-9007 10.1103/PhysRevLett.89.170405.
O. Bohigas, M. J. Giannoni, and C. Schmit, Characterization of chaotic quantum spectra and universality of level fluctuation laws, Phys. Rev. Lett. 52, 1 (1984) 0031-9007 10.1103/PhysRevLett.52.1.
E. P. Wigner, On the statistical distribution of the widths and spacings of nuclear resonance levels, Math. Proc. Cambridge Philos. Soc. 47, 790 (1951) 0305-0041 10.1017/S0305004100027237.
E. P. Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Ann. Math. 62, 548 (1955) 0003486X 10.2307/1970079.
F. J. Dyson, Statistical theory of the energy levels of complex systems. I, J. Math. Phys. 3, 140 (1962) 0022-2488 10.1063/1.1703773.
F. J. Dyson, Statistical theory of the energy levels of complex systems. II, J. Math. Phys. 3, 157 (1962) 0022-2488 10.1063/1.1703774.
F. J. Dyson, Statistical theory of the energy levels of complex systems. III, J. Math. Phys. 3, 166 (1962) 0022-2488 10.1063/1.1703775.
F. J. Dyson, The threefold way. Algebraic structure of symmetry groups and ensembles in quantum mechanics, J. Math. Phys. 3, 1199 (1962) 0022-2488 10.1063/1.1703863.
A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55, 1142 (1997) 0163-1829 10.1103/PhysRevB.55.1142.
M. L. Mehta, Random Matrices, 3rd ed. (Elsevier, San Diego, 2004).
F. Haake, Quantum Signatures of Chaos (Springer, Berlin, 2010).
G. Livan, M. Novaes, and P. Vivo, Introduction to Random Matrices-Theory and Practice (Springer, New York, 2018).
T. Can, Random Lindblad dynamics, J. Phys. A: Math. Theor. 52, 485302 (2019) 1751-8113 10.1088/1751-8121/ab4d26.
S. Denisov, T. Laptyeva, W. Tarnowski, D. Chruściński, and K. Zyczkowski, Universal spectra of random Lindblad operators, Phys. Rev. Lett. 123, 140403 (2019) 0031-9007 10.1103/PhysRevLett.123.140403.
T. Can, V. Oganesyan, D. Orgad, and S. Gopalakrishnan, Spectral gaps and midgap states in random quantum master equations, Phys. Rev. Lett. 123, 234103 (2019) 0031-9007 10.1103/PhysRevLett.123.234103.
L. Sá, P. Ribeiro, and T. Prosen, Spectral and steady-state properties of random Liouvillians, J. Phys. A: Math. Theor. 53, 305303 (2020) 1751-8113 10.1088/1751-8121/ab9337.
K. Wang, F. Piazza, and D. J. Luitz, Hierarchy of relaxation timescales in local random Liouvillians, Phys. Rev. Lett. 124, 100604 (2020) 0031-9007 10.1103/PhysRevLett.124.100604.
L. Sá, P. Ribeiro, and T. Prosen, Complex spacing ratios: A signature of dissipative quantum chaos, Phys. Rev. X 10, 021019 (2020) 10.1103/PhysRevX.10.021019.
A. del Campo and T. Takayanagi, Decoherence in conformal field theory, J. High Energy Phys. 02 (2020) 170 1029-8479 10.1007/JHEP02(2020)170.
Y.-N. Zhou, L. Mao, and H. Zhai, Rényi entropy dynamics and Lindblad spectrum for open quantum systems, Phys. Rev. Res. 3, 043060 (2021) 2643-1564 10.1103/PhysRevResearch.3.043060.
J. Cornelius, Z. Xu, A. Saxena, A. Chenu, and A. del Campo, Spectral filtering induced by non-Hermitian evolution with balanced gain and loss: Enhancing quantum chaos, Phys. Rev. Lett. 128, 190402 (2022) 0031-9007 10.1103/PhysRevLett.128.190402.
A. S. Matsoukas-Roubeas, F. Roccati, J. Cornelius, Z. Xu, A. Chenu, and A. del Campo, Non-Hermitian Hamiltonian deformations in quantum mechanics, J. High Energy Phys. 01 (2023) 060 1029-8479 10.1007/JHEP01(2023)060.
L. Sá, P. Ribeiro, and T. Prosen, Symmetry classification of many-body Lindbladians: Tenfold way and beyond, Phys. Rev. X 13, 031019 (2023) 10.1103/PhysRevX.13.031019.
K. Kawabata, A. Kulkarni, J. Li, T. Numasawa, and S. Ryu, Symmetry of open quantum systems: Classification of dissipative quantum chaos, PRX Quantum 4, 030328 (2023) 2691-3399 10.1103/PRXQuantum.4.030328.
K. Kawabata, Z. Xiao, T. Ohtsuki, and R. Shindou, Singular-value statistics of non-Hermitian random matrices and open quantum systems, PRX Quantum 4, 040312 (2023) 2691-3399 10.1103/PRXQuantum.4.040312.
A. S. Matsoukas-Roubeas, M. Beau, L. F. Santos, and A. del Campo, Unitarity breaking in self-averaging spectral form factors, Phys. Rev. A 108, 062201 (2023) 2469-9926 10.1103/PhysRevA.108.062201.
Y.-N. Zhou, T.-G. Zhou, and P. Zhang, General properties of the spectral form factor in open quantum systems, Front. Phys. 19, 31202 (2024) 10.1007/s11467-024-1406-7.
F. Ferrari, L. Gravina, D. Eeltink, P. Scarlino, V. Savona, and F. Minganti, Steady-state quantum chaos in open quantum systems, arXiv:2305.15479 [quant-ph].
A. M. García-García, L. Sá, J. J. M. Verbaarschot, and C. Yin, Towards a classification of pt-symmetric quantum systems: From dissipative dynamics to topology and wormholes, Phys. Rev. D 109, 105017 (2024) 10.1103/PhysRevD.109.105017.
M. Beau and A. del Campo, Nonlinear quantum metrology of many-body open systems, Phys. Rev. Lett. 119, 010403 (2017) 0031-9007 10.1103/PhysRevLett.119.010403.
J. Ginibre, Statistical ensembles of complex, quaternion, and real matrices, J. Math. Phys. 6, 440 (1965) 0022-2488 10.1063/1.1704292.
T. Kanazawa, Unitary matrix integral for QCD with real quarks and the GOE-GUE crossover, Phys. Rev. D 102, 034036 (2020) 2470-0010 10.1103/PhysRevD.102.034036.
T. Kanazawa, Unitary matrix integral for two-color QCD and the GSE-GUE crossover in random matrix theory, Phys. Lett. B 819, 136416 (2021) 0370-2693 10.1016/j.physletb.2021.136416.
H.-P. Breuer and P. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2007).
A. Rivas and S. F. Huelga, Open Quantum Systems: An Introduction (Springer, New York, 2012).
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, Cambridge, 2010).
R. Jozsa, Fidelity for mixed quantum states, J. Mod. Opt. 41, 2315 (1994) 0950-0340 10.1080/09500349414552171.
G. J. Milburn, Intrinsic decoherence in quantum mechanics, Phys. Rev. A 44, 5401 (1991) 1050-2947 10.1103/PhysRevA.44.5401.
I. L. Egusquiza, L. J. Garay, and J. M. Raya, Quantum evolution according to real clocks, Phys. Rev. A 59, 3236 (1999) 1050-2947 10.1103/PhysRevA.59.3236.
I. L. Egusquiza and L. J. Garay, Real clocks and the Zeno effect, Phys. Rev. A 68, 022104 (2003) 1050-2947 10.1103/PhysRevA.68.022104.
J. K. Korbicz, E. A. Aguilar, P. C¨wikliński, and P. Horodecki, Generic appearance of objective results in quantum measurements, Phys. Rev. A 96, 032124 (2017) 2469-9926 10.1103/PhysRevA.96.032124.
D. Lidar, A. Shabani, and R. Alicki, Conditions for strictly purity-decreasing quantum Markovian dynamics, Chem. Phys. 322, 82 (2006) 0301-0104 10.1016/j.chemphys.2005.06.038.
R. Horn and C. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1985).
A. M. García-García, Y. Jia, D. Rosa, and J. J. M. Verbaarschot, Replica symmetry breaking in random non-Hermitian systems, Phys. Rev. D 105, 126027 (2022) 2470-0010 10.1103/PhysRevD.105.126027.
B. Collins and P. Śniady, Integration with respect to the haar measure on unitary, orthogonal and symplectic group, Commun. Math. Phys. 264, 773 (2006) 0010-3616 10.1007/s00220-006-1554-3.
B. Collins and S. Matsumoto, On some properties of orthogonal Weingarten functions, J. Math. Phys. 50, 113516 (2009) 0022-2488 10.1063/1.3251304.
G. Akemann, J. Baik, and P. Di Francesco, The Oxford Handbook of Random Matrix Theory (Oxford University Press, New York, 2011).
M. Gessner and H.-P. Breuer, Generic features of the dynamics of complex open quantum systems: Statistical approach based on averages over the unitary group, Phys. Rev. E 87, 042128 (2013) 1539-3755 10.1103/PhysRevE.87.042128.
J. S. Cotler, G. Gur-Ari, M. Hanada, J. Polchinski, P. Saad, S. H. Shenker, D. Stanford, A. Streicher, and M. Tezuka, Black holes and random matrices, J. High Energy Phys. 05 (2017) 118 1029-8479 10.1007/JHEP05(2017)118.