  We study photon-photon correlations and entanglement generation in a
one-dimensional waveguide coupled to two qubits with an arbitrary spatial
separation. We develop a novel Green function method to study vacuum-mediated
qubit-qubit interactions, including both spontaneous and coherent couplings. As
a result of these interactions, quantum beats appear in the second-order
correlation function. We go beyond the Markovian regime and observe that such
quantum beats persist much longer than the qubit life time. Using these
non-Markovian processes, a high degree of long-distance entanglement can be
generated, making waveguide-QED systems promising candidates for scalable
quantum networking.
