For quantum state Procrustes optimization, restricting projective measurements to an r-dimensional subspace costs at most c log(r)^4 in objective value, independent of the ambient dimension.
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The suboptimality ratio of projective measurements restricted to low-rank subspaces
For quantum state Procrustes optimization, restricting projective measurements to an r-dimensional subspace costs at most c log(r)^4 in objective value, independent of the ambient dimension.