Entanglement Between Qubits via Qudit Spins in DMS Materials

Diluted magnetic semiconductors (DMS) are hybrid materials for spintronics, where magnetic impurities coupled to itinerant carriers allow for spin-dependent quantum control. In this work, we investigate a DMS quantum dot system modeled as a tripartite configuration ($\text{A--B--C}$)} consisting of two electronic spin qubits ($\text{A}$ and $\text{B}$) coupled to a high-spin Manganese (Mn) impurity ($S=5/2$) acting as a qudit mediator (C). The total dynamics, including decoherence effects, are obtained using the Lindblad master equation formalism.

We analyze the time evolution of an initially separable state, $\ket{\uparrow}_A \otimes \ket{\downarrow}_B$, observing the rapid formation of a strongly entangled state between the electronic qubits driven by the exchange interaction with the Mn qudit. Quantification using concurrence and fidelity reveals a key finding from our comparative analysis across mediator spins ($S=1/2, 3/2, 5/2$): higher-spin mediators significantly favor the generation of stronger and more stable entanglement. Specifically, for $S=1/2$ and $3/2$, the exchange coupling results in a denser energy level structure around the computational subspace. This quasi-degeneracy facilitates population leakage and dilution into parasitic auxiliary states, which severely weakens the qubit-qubit entanglement. In contrast, the $S=5/2$ spin offers a larger energy separation (gap), rendering these leakage pathways minimally relevant and resulting in superior and more persistent bipartite entanglement.

These findings establish the significant advantage of using high-spin Mn qudits in DMS structures as highly efficient and robust mediators for scalable spintronic quantum architectures.