Krylov complexity and gluon cascades in the high energy limit

We point out an interesting connection between the mathematical framework of the Krylov basis used for quantifying quantum complexity and 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 Krylov entropy matches entanglement entropy computations of {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.