Quantum Speed Limits For Adiabatic Evolution, Loschmidt Echo and Beyond

N. Il’in, O. Lychkovskiy

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    One often needs to estimate how fast an evolving state of a quantum system can depart from some target state or target subspace of a Hilbert space. Such estimates are known as quantum speed limits. We derive a quantum speed limit for a general time-dependent target subspace. When the target subspace is an instantaneous invariant subspace of a time-dependent Hamiltonian, the obtained quantum speed limit bounds the adiabatic fidelity, which is a figure of merit of quantum adiabaticity. We also compare two states evolving under two different Hamiltonians and derive a bound on the Loschmidt echo.

    Original languageEnglish
    Pages (from-to)640-649
    Number of pages10
    JournalInternational Journal of Theoretical Physics
    Issue number2
    Publication statusPublished - Feb 2021


    • Adiabatic evolution
    • Quantum speed limits
    • Quantum theory


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