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I have two questions regarding multipartite entanglement. For simplicity, consider a tripartite pure state $|\psi\rangle_{ABC}$. My questions are :

  1. How to find out if A and B are entangled with each other?

  2. Does the entanglement between each pair of the parties being 0 imply that the state $|\psi\rangle_{ABC}$ is separable?

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on 1) To analyze the entanglement of the subsystem AB you first trace out (ignore) system C, $\rho_{AB}=\mathrm{tr}_C | \psi_{ABC} \rangle\langle \psi_{ABC} |$. Then you can use an entanglement witness or calculate an entanglement measure. This is a review on entanglement.
on 2) A state can be entangled despite every bipartition being separable! Here's an example.

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