Abstract
We consider a partial trace transformation which maps a multipartite quantum state to collection of local density matrices. We call this collection a mean field state. The necessary and sufficient conditions under which a mean field state is compatible with at least one multipartite pure state are found for the system of qubits and for the tripartite system with the Hilbert space of dimension 2x2x4. Compatibility of mean field states with more general classes of multipartite quantum states is discussed.
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