Symmetric extendibility of quantum states

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Imagine that Alice and Bob share a quantum state, from which they want to distill something useful like entanglement or secret key. For this they need to communicate classically and they want to do this by one way communication from Alice to Bob. For some states, it might happen that the state is a part of a tripartite state shared with Charlie, which is invariant if Bob's and Charlie's systems are switched. Such a state is called a symmetric extension, and if it exists Alice and Bob have no chance of distilling key or entanglement by one way communication. I will present some results characterizing which quantum states have symmetric extension.