Noise-robust entanglement indicator for two-qubit mixed states: Engineering design for real-time monitoring in noisy quantum key distribution

Real-time monitoring of weak entanglement in noisy fiber links is a practical bottleneck for entanglement-based quantum key distribution (QKD). Standard concurrence and negativity vanish with vanishing gradient near the separability boundary and are not optimized for hardware-level line-rate monitoring. We propose a closed-form, noise-robust entanglement indicator [Formula: see text] for two-qubit mixed states, constructed by regularizing the Wootters concurrence with a determinant-based spectral penalty. [Formula: see text] requires no iterative optimization, retains a nonvanishing gradient along typical QKD noise trajectories, and has an average computation time of 0.189 ms per state. Numerical simulations over 100,000 random states show strong linear correlation with negativity (Pearson 0.986) and entanglement of formation (0.968). Under 12 common LOCC channels relevant to QKD, [Formula: see text] is nonincreasing in 100% of tested cases. A field-programmable gate array (FPGA) implementation achieves 210 ns latency, enabling real-time link health monitoring in metropolitan QKD networks.