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Multipartite states under local unitary transformations

Sergio Albeverio·Laura Cattaneo·Shao-Ming Fei·Xiao-Hong Wang
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Abstract

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.

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Sergio Albeverio, Laura Cattaneo, Shao-Ming Fei, Xiao-Hong Wang. 2005-12-12. Multipartite states under local unitary transformations. https://doi.org/10.1016/s0034-4877(05)80089-8

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