| __Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations__ *(Site not responding. Last check: 2007-09-16)* |

| | Using **Lie** theory, we generalize this to an n-qubit **decomposition**, the concurrence canonical **decomposition** (CCD) SU(2{sup n})=KAK. |

| | The **group** K fixes a bilinear form related to the concurrence, and in particular any unitary in K preserves the tangle vertical bar <{phi} vertical bar (-i{sigma}{sub 1}{sup y}){center_dot}{center_dot}{center_dot}(-i{sigma}{sub n}{sup y}) vertical bar {phi}> vertical bar{sup 2} for n even. |

| | Thus, the CCD shows that any n-qubit unitary is a composition of a unitary operator preserving this n-tangle, a unitary operator in A which applies relative phases to a set of GHZ states, and a second unitary operator which preserves the tangle. |

| www.osti.gov /energycitations/product.biblio.jsp?osti_id=20547162 (403 words) |