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A resource theory of entanglement with a unique multipartite maximally entangled state de Vicente, Julio


Entanglement theory is usually formulated as a quantum resource theory in which the free operations are local operations and classical communication (LOCC). This defines a partial order among bipartite pure states that makes it possible to identify a maximally entangled state, which turns out to be the most relevant state in applications. However, the situation changes drastically in the multipartite regime. Not only do there exist inequivalent forms of entanglement forbidding the existence of a unique maximally entangled state, but recent results have shown that LOCC induces a trivial ordering: almost all pure entangled multipartite states are incomparable (i.e. LOCC transformations among them are almost never possible). In order to cope with this problem I will consider alternative resource theories in which I relax the class of LOCC to operations that do not create entanglement. In more detail, I will consider two possible theories depending on whether resources correspond to multipartite entangled or genuinely multipartite entangled (GME) states and I will show that they are both non-trivial: they induce a meaningful partial order since every pure state is deterministically transformable to more weakly entangled pure states. Moreover, I will also show that no inequivalent forms of entanglement exist in these theories (i.e. all resource states are interconvertible with non-zero probability). Last but not least, I will prove that the resource theory of GME that I formulate here has a unique maximally entangled state, the generalized GHZ state, which can be transformed deterministically to any other state by the allowed free operations.

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