Entanglement Swapping for Partially Entangled Qudits and the Role of Quantum Complementarity

Abstract The entanglement swapping protocol (ESP) is extended to partially entangled qudit states and the process within the framework of complete complementarity relations (CCRs) is analyzed. Building on previous results for qubits, it is shown that the average distributed entanglement between two parties via ESP is bounded above by the initial entanglement of one of the input pairs, and also by the product of the initial entanglements. Notably, it is found that using initial states with vanishing local quantum coherence is sufficient to capture the essential features of the protocol, simplifying the analysis. By exploring the cases of qubits and qutrits, it is observed that the upper bound on the average distributed entanglement—expressed in terms of the product of the initial entanglements—can be improved, and what this tighter bound might be is conjectured. Finally, the role of quantum complementarity in the ESP is discussed and how local predictability constrains the entanglement that can be operationally distributed via ESP is shown.