Quantum Speed Limits to Operator Growth
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 unita...
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| Médium: | Elektronický zdroj E-kniha |
| Jazyk: | angličtina |
| Vydáno: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
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| Vydání: | 1st ed. 2024. |
| Edice: | Springer Theses, Recognizing Outstanding Ph.D. Research,
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| On-line přístup: | https://doi.org/10.1007/978-3-031-74179-1 |
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| Shrnutí: | 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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| Fyzický popis: | XV, 137 p. 9 illus., 6 illus. in color. online resource. |
| ISBN: | 9783031741791 |
| ISSN: | 2190-5061 |
| DOI: | 10.1007/978-3-031-74179-1 |