Glossary

Classical Information: Information encoded in a physical system who’s evolution is described via the laws of classical physics.

LOCC: This set of operations are often taken to be the allowed operations of the resource theory of entanglement.

Prime Dimensions: This appear to be the case as $N=2$ systems have to be treated differently, and hence all factors of 2 in a $d$-dimensional (not prime $d$) systems would also need to be treated differently.

multiplicity: the number of different eigenvectors that a given degenerate eigenvalue corresponds to.

Orthogonal Complement: The orthogonal complement of a vector space $V$ is the set of vectors orthogonal to all vectors in $V$.

Rotation Matrix: A matrix $O$ is a rotation matrix if its is orthogonal, $OO^t=O^tO=\mathbb{I}$, real, and has determinant 1, $\mathrm{Det}(O)=1$.