Entanglement of subspaces and error-correcting codes
Gilad Gour, Nolan R. Wallach · Physical Review A · 2007
We introduce the notion of entanglement of subspaces as a measure that quantifies the entanglement of bipartite states in a randomly selected subspace. We discuss its properties and in particular we show that for maximally entangled subspaces it is additive. Furthermore, we show that maximally entangled subspaces can play an important role in the study of quantum error-correction codes. We discuss both degenerate and nondegenerate codes and show that the subspace spanned by the logical code words of a nondegenerate code is a $k$-totally- (maximally) entangled subspace. As for non-degenerate codes, we provide a mathematical definition in terms of subspaces and, as an example, we analyze Shor's 9-qubit code in terms of 22 mutually orthogonal subspaces.