  We demonstrate how quantum entanglement can be directly witnessed in the
quasi-1D Heisenberg antiferromagnet KCuF$_3$. We apply three entanglement
witnesses --- one-tangle, two-tangle, and quantum Fisher information --- to its
inelastic neutron spectrum, and compare with spectra simulated by
finite-temperature density matrix renormalization group (DMRG) and classical
Monte Carlo methods. We find that each witness provides direct access to
entanglement. Of these, quantum Fisher information is the most robust
experimentally, and indicates the presence of at least bipartite entanglement
up to at least 50 K, corresponding to around 10% of the spinon zone-boundary
energy. We apply quantum Fisher information to higher spin-S Heisenberg chains,
and show theoretically that the witnessable entanglement gets suppressed to
lower temperatures as the quantum number increases. Finally, we outline how
these results can be applied to higher dimensional quantum materials to witness
and quantify entanglement.
