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We investigate the proposal by Kharzeev and Levin of a maximally entangledproton wave function in Deep Inelastic Scattering at low $x$ and the proposedrelation between parton number and final state hadron multiplicity. Contrary tothe original formulation we determine partonic entropy from the sum of gluonand quark distribution functions at low $x$, which we obtain from anunintegrated gluon distribution subject to next-to-leading orderBalitsky-Fadin-Kuraev-Lipatov evolution. We find for this framework very goodagreement with H1 data. We furthermore provide a comparison based on NNPDFparton distribution functions at both next-to-next-to-leading order andnext-to-next-to-leading with small $x$ resummation, where the latter providesan acceptable description of data.

Evidence for the maximally entangled low $x$ proton in Deep Inelastic Scattering from H1 data