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A strongly coupled Heisenberg chain provides an important channel for quantumcommunication through its many-body ground state. Yet, the nature of theeffective interactions and the ability to mediate long-range entanglementdiffers significantly for chains of opposite parity. Here, we contrast thecharacters of even and odd-size chains when they are coupled to externalqubits. Additional parity effects emerge in both cases, depending on thepositions of the attached qubits. Some striking results include (i) theemergence of maximal entanglement and (ii) Ruderman-Kittel-Kasuya-Yosida (RKKY)interactions for qubits attached to an even chain, and (iii) the ability ofchains of either parity to mediate qubit entanglement that is undiminished bydistance.

Even-Odd Effects of Heisenberg Chains on Long-range Interaction and Entanglement