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Quantum physics dictates fundamental speed limits during time evolution. Wepresent a quantum speed limit governing the generation of nonclassicality andthe mutual incompatibility of two states connected by time evolution. Thisresult is used to characterize the timescale required to generate a givenamount of quantumness under an arbitrary physical process. The bound is shownto be tight under pure dephasing dynamics. More generally, our analysis revealsthe dependence on the initial state and non-Markovian effects.

Fundamental Speed Limits to the Generation of Quantumness