Multipartite states under local unitary transformations
Albeverio, S, Cattaneo, L, Fei, S M, Wang, X H · CERN Document Server (European Organization for Nuclear Research) · 2005
The equivalence problem under local unitary transformation for $n$--partite pure states is reduced to the one for $(n-1)$--partite mixed states. In particular, a tripartite system $\\mathcal{H}_A\\otimes\\mathcal{H}_B\\otimes\\mathcal{H}_C$, where $\\mathcal{H}_j$ is a finite dimensional complex Hilbert space for $j=A,B,C$, is considered and a set of invariants under local transformations is introduced, which is complete for the set of states whose partial trace with respect to $\\mathcal{H}_A$ belongs to the class of generic mixed states.