Entanglement transitivity problems

Abstract One of the goals science is to understand relation between a whole and its parts, as exemplified by problem certifying entanglement system from knowledge reduced states. Here, we focus on different but related question: can collection marginal information reveal new information? We answer this affirmatively show that (non-) entangled states may exhibit (meta)transitivity entanglement, i.e., implying target must be entangled. By showing global n -qubit state compatible with certain two-qubit marginals in tree form unique, prove transitivity exists for involving an arbitrarily large number qubits. also completely characterize—in sense providing both necessary sufficient conditions—when occur tripartite scenario when two-qudit given are either Werner or isotropic Our numerical results suggest scenario, generic among derived pure