Entanglement of assistance and multipartite state distillation

By John A. Smolin, Frank Verstraete, Andreas J. Winter. 2005

141 citations recorded by the source corpus.

We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal Einstein-Podolsky-Rosen (EPR) pair distillation procedure for a given tripartite pure state, and we show that it actually yields EPR and Greenberger-Horne-Zeilinger (GHZ) states; in fact, under a restricted class of protocols, which we call "one-way broadcasting," the GHZ rate is shown to be optimal. This result implies a capacity theorem for quantum channels where the environment helps transmission by broadcasting the outcome of an optimally chosen measurement. We discuss generalizations to m parties and show (for m=4) that the maximal amount of entanglement that can be localized between two parties is given by the smallest entropy of a group of parties of which the one party is a member, but not the other. This gives an explicit expression for the asymptotic localizable entanglement and shows that any nontrivial ground state of a spin system can be used as a perfect quantum repeater if many copies are available in parallel. Finally, we provide evidence that any unital channel is asymptotically equivalent to a mixture of unitaries and any general channel to a mixture of partial isometries.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/1799bc84cf48d92955cbd3696377692371614362

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Citations in the corpus

An Asymptotic Property of Factorizable Completely Positive Maps and the Connes Embedding Problem (2014, background): “[10]), where they provided evidence that every unital quantum channel might always be well approximated by a convex combination of unitarily implemented ones.”
Holographic duality from random tensor networks (2016, methodology): “this upper bound was asymptotically achievable [46]:”
The mother of all protocols: restructuring quantum information’s family tree (2006, background): ““QMAC” refers to the task of sending quantum data through a quantum multiple access channel [12, 18], “broadcast” the task of sending quantum data through a quantum broadcast channel [17] and the environment-assisted quantum capacity is discussed in [19]. leads to more children.”
Partial quantum information (2005, background): “This problem was recently solved for up to four parties 23 , and can be generalized to an arbitrary number m of parties using state merging (using universal codes depending only on the density matrix of the helper, as described in Figure 1).”
Unital Quantum Channels – Convex Structure and Revivals of Birkhoff’s Theorem (2008, background): “Another remarkable step was made in Ref.[12] where evidence has been provided that asymptotically many copies of a unital channel might always be well approximated by a mixture of unitaries—a conjectured restoration of Birkhoff’s theorem in the asymptotic limit.”