entangled in two inequivalent ways
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Introduction
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The understanding of entanglement is at the very heart of Quantum Information Theory (QIT). In recent years, there has been an ongoing effort to characterize qualitatively and quantitatively the entanglement properties of multiparticle systems. A situation of particular interest in QIT consists of several parties that are spatially separated from each other and share a composite system in an entangled state. This setting conditionates the parties —which are typically allowed to communicate through a classical channel— to only act locally on their subsystems. But even restricted to local operations assisted with classical communication (LOCC), the parties can still modify the entanglement properties of the system and in particular they can try to convert an entangled state into another. This possibility leads to natural ways of defining equivalence relations in the set of entangled states —where equivalent states are then said to contain the same kind of entanglement—, also of establishing hierarchies between the resulting classes.

For instance, we could agree in identifying any two states which can be obtained from each other with certainty by means of LOCC. Clearly, this criterion is interesting in QIT because the parties 