  In an isolated system, the time evolution of a given observable in the
Heisenberg picture can be efficiently represented in Krylov space. In this
representation, an initial operator becomes increasingly complex as time goes
by, a feature that can be quantified by the Krylov complexity. We introduce a
fundamental and universal limit to the growth of the Krylov complexity by
formulating a Robertson uncertainty relation, involving the Krylov complexity
operator and the Liouvillian, as generator of time evolution. We further show
the conditions for this bound to be saturated and illustrate its validity in
paradigmatic models of quantum chaos.
