Fidelity analysis of path entangled two-quanton systems

Path (momentum) entanglement, arising from the spatial correlations of quantons, constitutes a cornerstone of quantum communication, metrology, and advanced interferometry. Despite its profound importance, the quantitative evaluation of path entanglement remains an intricate task, particularly under transformations imposed by interferometric setups. This study explores the fidelity of path entanglement in two interferometric configurations, P-BS and BS-P-BS, for spatially correlated two-quanton systems. Fidelity, which measures the preservation of quantum correlations, is analyzed alongside concurrence to capture the dynamics of entanglement under phase retarder manipulations. Our findings reveal contrasting behaviors between the two setups: while the P-BS configuration shows a decrease in fidelity with increasing concurrence, the BS-P-BS setup achieves maximum fidelity for maximally entangled states with carefully tuned retarder phases. These findings underscore the robustness of the BS-P-BS architecture in maintaining quantum correlations, rendering it a compelling candidate for quantum teleportation and high-fidelity quantum channel implementations. Furthermore, the interplay between retarder phases, concurrence, and fidelity offers novel insights for optimizing interferometric designs in advanced quantum information processing applications.