The theory of quantum information constitutes the functional value of the
quantum entanglement, i.e., quantum entanglement is essential for high fidelity
of quantum protocols, while fundamental physical processes behind the formation
of quantum entanglement are less relevant for practical purposes. In the
present work, we explore physical mechanisms leading to the emergence of
quantum entanglement in the initially disentangled system. In particular, we
analyze spin entanglement of outgoing electrons in a nonrelativistic quantum
(e,2e) collision on a target with one active electron. Our description
exploits the time-dependent scattering formalism for typical conditions of
scattering experiments, and contrary to the customary stationary formalism
operates with realistic scattering states. We quantify the spin entanglement in
the final scattering channel through the pair concurrence and express it in
terms of the experimentally measurable spin-resolved (e,2e) triple
differential cross sections. Besides, we consider Bell's inequality and inspect
the regimes of its violation in the final channel. We address both the pure and
the mixed initial spin state cases and uncover kinematical conditions of the
maximal entanglement of the outgoing electron pair. The numerical results for
the pair concurrence, entanglement of formation, and violation of Bell's
inequality obtained for the (e,2e) ionization process of atomic hydrogen show
that the entangled electron pairs indeed can be formed in the (e,2e)
collisions even with spin-unpolarized projectile and target electrons in the
initial channel. The positive entanglement balance---the difference between
entanglements of the initial and final electron pairs---can be measured in the
experiment.Comment: 31 pages, 6 figure