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Quantum speed limits to operator growth

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quantum speed limits to operator growthby Nicoletta Carabba.
Author:	Carabba, Nicoletta.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xv, 137 p. :ill. (some col.), digital ;24 cm.
Notes:	"Doctoral thesis accepted by the University of Luxembourg, Luxembourg, Luxembourg."
Contained By:	Springer Nature eBook
Subject:	Quantum theory.
Online resource:	https://doi.org/10.1007/978-3-031-74179-1
ISBN:	9783031741791$q(electronic bk.)

Quantum speed limits to operator growth
Carabba, Nicoletta.

Quantum speed limits to operator growth[electronic resource] /by Nicoletta Carabba. - Cham :Springer Nature Switzerland :2024. - xv, 137 p. :ill. (some col.), digital ;24 cm. - Springer theses,2190-5061. - Springer theses..

"Doctoral thesis accepted by the University of Luxembourg, Luxembourg, Luxembourg."

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.

ISBN: 9783031741791$q(electronic bk.)

Standard No.: 10.1007/978-3-031-74179-1doiSubjects--Topical Terms:

199020
Quantum theory.

LC Class. No.: QC174.12

Dewey Class. No.: 530.12

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505 0 $a 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.
520 $a 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.
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