We present a description of locally equivalent states in terms of symplectic geometry. Using the moment map between local orbits in the space of states and coadjoint orbits of the local unitary group we reduce the problem of local unitary equivalence to an easy part consisting of identifying the proper coadjoint orbit and a harder problem of the geometry of fibers of the moment map. We give a detailed analysis of the properties of orbits of "equally entangled states". In particular we show connections between certain symplectic properties of orbits such as their isotropy and coisotropy with effective criteria of local unitary equivalence.
Local equivalence of representations of Diff$^+(S^1)$ corresponding to different highest weights
Non-commutative Integrability, Moment Map and Geodesic Flows
Bipartite entanglement, spherical actions and geometry of local unitary orbits
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