  A strongly coupled Heisenberg chain provides an important channel for quantum
communication through its many-body ground state. Yet, the nature of the
effective interactions and the ability to mediate long-range entanglement
differs significantly for chains of opposite parity. Here, we contrast the
characters of even and odd-size chains when they are coupled to external
qubits. Additional parity effects emerge in both cases, depending on the
positions of the attached qubits. Some striking results include (i) the
emergence of maximal entanglement and (ii) Ruderman-Kittel-Kasuya-Yosida (RKKY)
interactions for qubits attached to an even chain, and (iii) the ability of
chains of either parity to mediate qubit entanglement that is undiminished by
distance.
