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On minimum reversible entanglement generating sets

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Every pure bipartite entangled state can be reversibly interconverted by local operations and classical communication into EPR pairs, in the limit of asymptotically many copies of the state. The problem of minimum reversible entanglement generating sets (MREGS) asks whether a similar situation occur for states of more parties, namely whether there is a finite set of states for which any pure entangled state can be reversibly interconverted into some of its elements.

In this talk it will be shown there is no finite MREGS in the restricted setting where only forward classical communication is allowed, e.g. from Alice to Bob and from Bob to Charlie in the three parties case.

Moreover, for the general case of unrestricted classical communication among the parties, we make partial progress in the problem and show that conditioned on the existence of infinitely many inequivalent classes of bipartite bound entangled states, there is no finite MREGS .

We also briefly discuss another application of our techniques to the interconvertability of zero-capacity quantum channels.

This talk is part of the CQIF Seminar series.

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