Extend the trace-invariant framework to multipartite systems

Develop the multipartite extension of the dimension-free trace-invariant inequality cones and derive the corresponding multipartite entanglement criteria for multipartite states.

Background

The framework developed in the paper concerns bipartite separable states, their local-unitary trace invariants, associated moment cones, and polar cones of valid inequalities. The authors note that the construction naturally suggests cones indexed by products of symmetric groups for multipartite systems.

The extension would require developing the corresponding multipartite invariant parametrization and determining criteria analogous to the PPT, realignment, and enhanced-realignment moment hierarchies. The paper explicitly defers this task.