If A is normal and A and B are traceless with ||A||_F^2+||B||_F^2=1/d, then the two largest squared singular values of A⊗I+I⊗B are bounded by (3d-4)/d^2.
Superdense coding of quantum states,
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A matrix inequality related to the entanglement distillation problem
If A is normal and A and B are traceless with ||A||_F^2+||B||_F^2=1/d, then the two largest squared singular values of A⊗I+I⊗B are bounded by (3d-4)/d^2.