aiqbench analysis

This research identifies a fundamental trade-off where maximizing Fisher sensitivity in bipartite SU(d) metrology inevitably creates $d(d-1)/2$ blind directions that become undetectable due to vanishing mean generator commutators. The study establishes that this constraint is not an information loss but a specific mathematical limit linked to weak compatibility and exchange symmetry, which causes the Holevo cost to diverge at optimal performance. Researchers propose using generalized GHZ probes with three or more particles as a viable path to overcome these limitations by satisfying weak compatibility while maintaining full local identifiability.