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arXiv · 1805.04083

Quantum speed limits for adiabatic evolution, Loschmidt echo and beyond

N. Il`in·O. Lychkovskiy
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Abstract

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.

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N. Il`in, O. Lychkovskiy. 2018-05-10. Quantum speed limits for adiabatic evolution, Loschmidt echo and beyond. https://doi.org/10.1007/s10773-020-04458-5

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