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Requirements for compatibility between local and multipartite quantum states

Sergey Bravyi
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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 $n$ 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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Sergey Bravyi. 2003-01-06. Requirements for compatibility between local and multipartite quantum states. https://arxiv.org/abs/quant-ph/0301014

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