Speed limit for open quantum systems. (arXiv:1810.03011v2 [quant-ph] UPDATED)

We study the quantum speed limit for open quantum systems described by the
Lindblad master equation. The obtained inequality shows a trade-off relation
between the operation time and the physical quantities such as the energy
fluctuation and the entropy production. We further identify a quantity
characterizing the speed of the state transformation, which appears only when
we consider the open system dynamics in the quantum regime. When the thermal
relaxation is dominant compared to the unitary dynamics of the system, we show
that this quantity is approximated by the energy fluctuation of the
counter-diabatic Hamiltonian which is used as a control field in the shortcuts
to adiabaticity protocol. We discuss the physical meaning of the obtained
quantum speed limit and try to give better intuition about the speed in open
quantum systems.

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