  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.
