  Top quarks represent unique high-energy systems since their spin correlations
can be measured, thus allowing to study fundamental aspects of quantum
mechanics with qubits at high-energy colliders. We present here the general
framework of the quantum state of a top-antitop ($t\bar{t}$) quark pair
produced through quantum chromodynamics (QCD) in a high-energy collider. We
argue that, in general, the total quantum state that can be probed in a
collider is given in terms of the production spin density matrix, which
necessarily gives rise to a mixed state. We compute the quantum state of a
$t\bar{t}$ pair produced from the most elementary QCD processes, finding the
presence of entanglement and CHSH violation in different regions of phase
space. We show that any realistic hadronic production of a $t\bar{t}$ pair is a
statistical mixture of these elementary QCD processes. We focus on the
experimentally relevant cases of proton-proton and proton-antiproton
collisions, performed at the LHC and the Tevatron, analyzing the dependence of
the quantum state with the energy of the collisions. We provide experimental
observables for entanglement and CHSH-violation signatures. At the LHC, these
signatures are given by the measurement of a single observable, which in the
case of entanglement represents the violation of a Cauchy-Schwarz inequality.
We extend the validity of the quantum tomography protocol for the $t\bar{t}$
pair proposed in the literature to more general quantum states, and for any
production mechanism. Finally, we argue that a CHSH violation measured in a
collider is only a weak form of violation of Bell's theorem, necessarily
containing a number of loopholes.
