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We consider the perturbative (weak field) limit of the small $x$ QCDevolution equation for quadrupole, the normalized trace of four Wilson lines inthe fundamental representation, which appears in di-hadron angular correlationin high energy collisions. We linearize the quadrupole evolution equation andthen expand the Wilson lines in powers of $g\, A_{\mu}$ where $A_{\mu}$ is thegauge field. The quadratic terms in the expansion ($\sim g^2\, A^2$) satisfythe BFKL equation as has been recently shown. We then consider the quarticterms ($\sim g^4\, A^4$) in the expansion and show that the linearizedquadrupole evolution equation, written in terms of color charge density $\rho$,reduces to the well-known BJKP equation for the imaginary part offour-reggeized gluon exchange amplitude. We comment on the possibility that theBJKP equation for the evolution of a $n$-reggeized gluon state can be obtainedfrom the JIMWLK evolution equation for the normalized trace of $n$ fundamentalWilson lines when non-linear (recombination) terms are neglected.

On perturbative limits of quadrupole evolution in QCD at high energy