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MiS Preprint

Multipartite States under Local Unitary Transformations

Sergio Albeverio, Laura Cattaneo, Shao-Ming Fei and Xiao-Hong Wang


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.

tripartite quantum states, local unitary transformations, entanglement, invariants

Related publications

2005 Repository Open Access
Sergio Albeverio, Laura Cattaneo, Shao-Ming Fei and Xiao-Hong Wang

Multipartite states under local unitary transformations

In: Reports on mathematical physics, 56 (2005) 3, pp. 341-350