Effects of coherent and incoherent measurement imperfections on multipartite quantum nonlocality and quantum key distribution

Multipartite Bell nonlocality is a central resource for device-independent quantum information protocols, but its practical certification is inevitably affected by imperfect measurements. We analyze how coherent angular misalignment and incoherent outcome flipping affect Bell-value degradation and nonlocality thresholds in $n$-partite GHZ states based on the Mermin, Svetlichny, and Mermin–Ardehali–Belinskii–Klyshko (MABK) inequalities. Coherent misalignment produces periodic angular violation windows whose individual widths shrink with the number of parties. In contrast, incoherent outcome flipping yields a single critical outcome-flipping probability, which increases with $n$ for MABK and the odd-$n$ Mermin inequalities, but decreases with $n$ for the Svetlichny inequality. Connecting the degraded Bell values to asymptotic Devetak–Winter key-rate bounds under a convex-combination attack model shows that secret-key generation imposes stricter constraints on measurement imperfections than nonlocality certification. These results provide quantitative benchmarks for robust multipartite nonlocality certification and key-rate estimation under measurement imperfections.