Compatibility between local and multipartite states
Sergey Bravyi · Quantum Information and Computation · 2004
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. For the Hilbert spaces $(\CC^2)^{\otimes n}$ and $\CC^2\otimes\CC^2\otimes\CC^4$ the necessary and sufficient conditions under which a mean field state is compatible with at least one multipartite pure state are found. Compatibility of mean field states with more general classes of multipartite quantum states is discussed.