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This paper studies an optimization problem on the sum of traces of matrixquadratic forms on $m$ orthogonal matrices, which can be considered as ageneralization of the synchronization of rotations. While the problem isnonconvex, the paper shows that its semidefinite programming relaxation cansolve the original nonconvex problems exactly, under an additive noise modelwith small noise in the order of $O(-m^{1/4})$, where $m$ is the number oforthogonal matrices. This result can be considered as a generalization ofexisting results on phase synchronization.

Tightness of the semidefinite relaxation for orthogonal trace-sum maximization