03569nam a22005775i 4500 978-3-031-74179-1 DE-He213 20251030114937.0 cr nn 008mamaa 250201s2024 sz | s |||| 0|eng d 9783031741791 978-3-031-74179-1 10.1007/978-3-031-74179-1 doi QC173.96-174.52 PHQ bicssc SCI057000 bisacsh PHQ thema Carabba, Nicoletta. author. aut http://id.loc.gov/vocabulary/relators/aut 90624 Quantum Speed Limits to Operator Growth [electronic resource] / by Nicoletta Carabba. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XV, 137 p. 9 illus., 6 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5061 Chapter 1.Introduction -- Chapter 2.Operator growth in Krylov space -- Chapter 3.Dispersion bound on Krylov complexity -- Chapter 4.A brief history of quantum speed limits in isolated systems -- Chapter 5.QSLs on operator flows -- Chapter 6. QSLs on correlation functions -- Chapter 7.A geometric operator quantum speed limit -- Chapter 8.Conclusions. This book introduces universal bounds to quantum unitary dynamics, with applications ranging from condensed matter models to quantum metrology and computation. Motivated by the observation that the dynamics of many-body systems can be better unraveled in the Heisenberg picture, we focus on the unitary evolution of quantum observables, a process known as operator growth and quantified by the Krylov complexity. By means of a generalized uncertainty relation, we constrain the complexity growth through a universal speed limit named the dispersion bound, investigating also its relation with quantum chaos. Furthermore, the book extends the framework of quantum speed limits (QSLs) to operator flows, identifying new fundamental timescales of physical processes. Crucially, the dynamics of operator complexity attains the QSL whenever the dispersion bound is saturated. Our results provide computable constraints on the linear response of many-body systems out of equilibrium and the quantum Fisher information governing the precision of quantum measurements. Quantum physics. 66608 System theory. 66519 Dynamical systems. Quantum electrodynamics. 70514 Quantum Physics. 66608 Quantum Measurement and Metrology. 67415 Complex Systems. 66520 Dynamical Systems. Quantum Electrodynamics, Relativistic and Many-body Calculations. 70517 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031741784 Printed edition: 9783031741807 Printed edition: 9783031741814 Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5061 66370 https://doi.org/10.1007/978-3-031-74179-1 ZDB-2-PHA ZDB-2-SXP 66608 66608