03200nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050002000153072001600173072002300189072001500212100008100227245009200308250001800400264006900418300006200487336002600549337002600575338003600601347002400637490007200661505035600733520106501089650002102154650001902175650002302194650002902217650002102246650003902267650002102306650002302327650007002350710003402420773002602454776003602480776003602516776003602552830007202588856004602660978-3-031-74179-1DE-He21320251030114937.0cr nn 008mamaa250201s2024    sz |    s    |||| 0|eng d  a97830317417917 a10.1007/978-3-031-74179-12doi 4aQC173.96-174.52 7aPHQ2bicssc 7aSCI0570002bisacsh 7aPHQ2thema1 aCarabba, Nicoletta.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aQuantum Speed Limits to Operator Growthh[electronic resource] /cby Nicoletta Carabba.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXV, 137 p. 9 illus., 6 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Theses, Recognizing Outstanding Ph.D. Research,x2190-50610 aChapter 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.  aThis 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. 0aQuantum physics. 0aSystem theory. 0aDynamical systems. 0aQuantum electrodynamics.14aQuantum Physics.24aQuantum Measurement and Metrology.24aComplex Systems.24aDynamical Systems.24aQuantum Electrodynamics, Relativistic and Many-body Calculations.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303174178408iPrinted edition:z978303174180708iPrinted edition:z9783031741814 0aSpringer Theses, Recognizing Outstanding Ph.D. Research,x2190-506140uhttps://doi.org/10.1007/978-3-031-74179-1