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Quantum Speed Limits to Operator Growth / by Nicoletta Carabba

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Theses, Recognizing Outstanding Ph.D. ResearchPublisher: Cham : Springer Nature Switzerland, 2024Publisher: Cham : Imprint: Springer, 2024Edition: 1st ed. 2024Description: 1 Online-Ressource(XV, 137 p. 9 illus., 6 illus. in color.)ISBN:
  • 9783031741791
Subject(s): Additional physical formats: 9783031741784 | 9783031741807 | 9783031741814 | Erscheint auch als: 9783031741784 Druck-Ausgabe | Erscheint auch als: 9783031741807 Druck-Ausgabe | Erscheint auch als: 9783031741814 Druck-AusgabeDDC classification:
  • 530.12 23
DOI: DOI: 10.1007/978-3-031-74179-1Online resources: Summary: 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.Summary: 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.PPN: PPN: 1916312454Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-PHA | ZDB-2-SXP
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