  We point out an interesting connection between the mathematical framework of
the Krylov basis, which is used to quantify quantum complexity, and the
entanglement entropy in high-energy QCD. In particular, we observe that the
cascade equation of the dipole model is equivalent to the $SL(2,R)$ Schrodinger
equation in the Krylov basis. Consequently, the Krylov complexity corresponds
to the average distribution of partons and the Krylov entropy is the
counterpart the entanglement entropy computations of \cite{Kharzeev:2017qzs}.
Our work not only brings new tools for exploring quantum information and
complexity in QCD, but also gives hope for experimental tests of some of the
recent, physical probes of quantum complexity.
