Physics – Quantum Physics
Scientific paper
2007-04-02
Phys. Rev. A 76, 042309 (2007)
Physics
Quantum Physics
8 pages, Published Version
Scientific paper
10.1103/PhysRevA.76.042309
We introduce the notion of entanglement of subspaces as a measure that quantify 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 non-degenerate codes and show that the subspace spanned by the logical codewords of a non-degenerate code is a 2k-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 nine qubits code in terms of 22 mutually orthogonal subspaces.
Gour Gilad
Wallach Nolan R.
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