TY - JOUR
T1 - Kolmogorov-Arnold-Moser Stability for Conserved Quantities in Finite-Dimensional Quantum Systems
AU - Burgarth, Daniel
AU - Facchi, Paolo
AU - Nakazato, Hiromichi
AU - Pascazio, Saverio
AU - Yuasa, Kazuya
N1 - Funding Information:
This research was funded in part by the Australian Research Council (Project No. FT190100106) and by the Top Global University Project from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. P. F. and S. P. were partially supported by Istituto Nazionale di Fisica Nucleare (INFN) through the project “QUANTUM.” P. F. and S. P. acknowledge support by MIUR via PRIN 2017 (Progetto di Ricerca di Interesse Nazionale), project Taming complexity via QUantum Strategies: a Hybrid Integrated Photonic approach (QUSHIP) (2017SRNBRK). P. F. was partially supported by the Italian National Group of Mathematical Physics (GNFM-INdAM). P. F. and S. P. were partially supported by Regione Puglia and by QuantERA ERA-NET Cofund in Quantum Technologies (Grant No. 731473), project Quantum Computing Solutions for High-Energy Physics (QuantHEP). H. N. is partly supported by the Institute for Advanced Theoretical and Experimental Physics, Waseda University, and by Waseda University Grant for Special Research Projects (Project No. 2020C-272). K. Y. was supported by the Grants-in-Aid for Scientific Research (C) (No. 18K03470) and for Fostering Joint International Research (B) (No. 18KK0073) both from the Japan Society for the Promotion of Science (JSPS).
Publisher Copyright:
© 2021 American Physical Society.
PY - 2021/4/12
Y1 - 2021/4/12
N2 - We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries, small perturbations can lead to large deviations over long times, while for robust symmetries, their expectation values remain close to their initial values for all times. This is in analogy with the celebrated Kolmogorov-Arnold-Moser theorem in classical mechanics. To prove this result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.
AB - We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries, small perturbations can lead to large deviations over long times, while for robust symmetries, their expectation values remain close to their initial values for all times. This is in analogy with the celebrated Kolmogorov-Arnold-Moser theorem in classical mechanics. To prove this result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.
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U2 - 10.1103/PhysRevLett.126.150401
DO - 10.1103/PhysRevLett.126.150401
M3 - Article
C2 - 33929214
AN - SCOPUS:85104386370
SN - 0031-9007
VL - 126
JO - Physical Review Letters
JF - Physical Review Letters
IS - 15
M1 - 150401
ER -