  Quantum entanglement is a fundamental property of quantum mechanics.
Recently, studies have explored entanglement in the $t\bar{t}$ system at the
Large Hadron Collider (LHC) when both the top quark and anti-top quark decay
leptonically. Entanglement is detected via correlations between the
polarizations of the top and anti-top and these polarizations are measured
through the angles of the decay products of the top and anti-top. In this work,
we propose searching for evidence of quantum entanglement in the semi-leptonic
decay channel where the final state includes one lepton, one neutrino, two
$b$-flavor tagged jets, and two light jets from the $W$ decay. We find that
this channel is both easier to reconstruct and has a larger effective quantity
of data than the fully leptonic channel. As a result, the semi-leptonic channel
is $60\%$ more sensitive to quantum entanglement and a factor of 3 more
sensitive to Bell inequality violation, compared to the leptonic channel. In
$139~{\rm fb}^{-1}$ ($3~{\rm ab}^{-1}$) of data at the LHC (HL-LHC), it should
be feasible to measure entanglement at a precision of $\lesssim 3\%\ (0.7\%)$.
Detecting Bell inequality violation, on the other hand, is more challenging.
With $300~{\rm fb}^{-1}$ ($3~{\rm ab}^{-1}$) of integrated luminosity at the
LHC Run-3 (HL-LHC), we expect a sensitivity of $1.3\sigma$ ($4.1 \sigma$). In
our study, we utilize a realistic parametric fitting procedure to optimally
recover the true angular distributions from detector effects. Compared to
unfolding this procedure yields more stable results.
