Quantum Speed Limits On Operator Flows And Correlation Functions

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Nicoletta Carabba¹, Niklas Hörnedal^1,2, and Adolfo del Campo^1,3

¹Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, G. D. Luxembourg
²Fysikum, Stockholms Universitet, 106 91 Stockholm, Sweden
³Donostia International Physics Center, E-20018 San Sebastián, Spain

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Abstract

Quantum speed limits (QSLs) identify fundamental time scales of physical processes by providing lower bounds on the rate of change of a quantum state or the expectation value of an observable. We introduce a generalization of QSL for unitary operator flows, which are ubiquitous in physics and relevant for applications in both the quantum and classical domains. We derive two types of QSLs and assess the existence of a crossover between them, that we illustrate with a qubit and a random matrix Hamiltonian, as canonical examples. We further apply our results to the time evolution of autocorrelation functions, obtaining computable constraints on the linear dynamical response of quantum systems out of equilibrium and the quantum Fisher information governing the precision in quantum parameter estimation.

Popular summary

The nature of time has always been one of the most debated subjects in human history, involving and relating different areas of human knowledge. In quantum physics, time, rather than being an observable as the position, is treated as a parameter. Accordingly, the Heisenberg uncertainty principle and time-energy uncertainty relation are of a deeply different nature. In 1945 the latter was refined by Mandelstam and Tamm as a quantum speed limit (QSL), that is, a lower bound on the time needed for the quantum state of a physical system to evolve into a distinguishable state. This new vision gave rise to a prolific series of works extending the notion of QSL to different kinds of quantum states and physical systems. Despite decades of research, QSL to date remains focused on quantum state distinguishability, natural for applications such as quantum computing and metrology. Yet, other applications involve operators flowing or evolving as a function of time. In this context, conventional QSL are inapplicable.

In this work we introduce a new class of QSL formulated for unitary operator flows. We generalize the celebrated Mandelstam-Tamm and Margolus-Levitin speed limits to operator flows, demonstrate their validity in simple and complex systems and illustrate their relevance to bound response functions in condensed matter physics. We expect our findings to find further applications including the dynamics of integrable systems, renormalization group and quantum complexity, among other examples.

► BibTeX data

@article{Carabba2022quantumspeedlimits, doi = {10.22331/q-2022-12-22-884}, url = {https://doi.org/10.22331/q-2022-12-22-884}, title = {Quantum speed limits on operator flows and correlation functions}, author = {Carabba, Nicoletta and H{“{o}}rnedal, Niklas and Campo, Adolfo del}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {6}, pages = {884}, month = dec, year = {2022}<br /> }

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Cited by

[1] Mir Afrasiar, Jaydeep Kumar Basak, Bidyut Dey, Kunal Pal, and Kuntal Pal, “Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model”, arXiv:2208.10520.

[2] Farha Yasmin and Jan Sperling, “Entanglement-assisted quantum speedup: Beating local quantum speed limits”, arXiv:2211.14898.

The above citations are from SAO/NASA ADS (last updated successfully 2022-12-23 04:22:47). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2022-12-23 04:22:45).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Source: https://quantum-journal.org/papers/q-2022-12-22-884/

Time Stamp: December 22, 2022

Time Stamp: Jun 12, 2023

Quantum speed limits on operator flows and correlation functions

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