03505nam 22006735 450 991097797940332120250201115242.09783031741791303174179X10.1007/978-3-031-74179-1(CKB)37447379700041(MiAaPQ)EBC31897173(Au-PeEL)EBL31897173(OCoLC)1496393810(DE-He213)978-3-031-74179-1(EXLCZ)993744737970004120250201d2024 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierQuantum Speed Limits to Operator Growth /by Nicoletta Carabba1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (222 pages)Springer Theses, Recognizing Outstanding Ph.D. Research,2190-50619783031741784 3031741781 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.Springer Theses, Recognizing Outstanding Ph.D. Research,2190-5061Quantum theorySystem theoryDynamicsQuantum electrodynamicsQuantum PhysicsQuantum Measurement and MetrologyComplex SystemsDynamical SystemsQuantum Electrodynamics, Relativistic and Many-body CalculationsQuantum theory.System theory.Dynamics.Quantum electrodynamics.Quantum Physics.Quantum Measurement and Metrology.Complex Systems.Dynamical Systems.Quantum Electrodynamics, Relativistic and Many-body Calculations.530.12Carabba Nicoletta1788708MiAaPQMiAaPQMiAaPQBOOK9910977979403321Quantum Speed Limits to Operator Growth4323872UNINA