LAUSR

Parton distributions can be defined in terms of the entropy of entanglement between the spatial region probed by deep inelastic scattering (DIS) and the rest of the proton. This approach leads to a simple relation $S = \ln[xG(x)]$ between the gluon structure function $xG(x)$ and the entropy of the produced hadronic state $S$; it is valid at sufficiently small Bjorken $x$, where gluons dominate and the proton becomes a maximally entangled state.Recently, the H1 Collaboration analyzed the entropy of the hadronic state in DIS, and studied its relation to the gluon structure function; poor agreement with the predicted relation was found.Here we show that the data from the H1 Collaboration in fact agree well with the prediction based on entanglement, once two important effects are taken into account: i) because the hadron multiplicity $N$ in the H1 measurement is not large, $\sim 1/N$ corrections to the predicted relation have to be included; and ii) since the measured hadrons are mostly inthe current fragmentation region, the relevant structure function is not the gluon but the sea quark one.