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arXiv:quant-ph/0611081 · Physical Review A

Superadditivity of distillable entanglement from quantum teleportation

Somshubhro Bandyopadhyay, Vwani Roychowdhury

Published Dec 7, 2005• 7 citations
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Abstract

We show that the phenomenon of superadditivity of distillable entanglement observed in multipartite quantum systems results from the consideration of states created during the execution of the standard end-to-end quantum teleportation protocol [and a few additional local operations and classical communication (LOCC) steps] on a linear chain of singlets. Some of these intermediate states are tensor products of bound entangled (BE) states, and hence, by construction possess distillable entanglement, which can be unlocked by simply completing the rest of the LOCC operations required by the underlying teleportation protocol. We use this systematic approach to construct both new and known examples of superactivation of bound entanglement, and examples of activation of BE states using other BE states. A surprising outcome is the construction of noiseless quantum relay channels with no distillable entanglement between any two parties, except for that between the two end nodes.

DOI
10.1103/physreva.72.060303

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We show that the phenomenon of superadditivity of distillable entanglement observed in multipartite quantum systems results from the consideration of states created during the execution of the standard end-to-end quantum teleportation protocol [and a few additional local operations and classical communication (LOCC) steps] on a linear chain of singlets. Some of these intermediate states are tensor products of bound entangled (BE) states, and hence, by construction possess distillable entanglement, which can be unlocked by simply completing the rest of the LOCC operations required by the underlying teleportation protocol. We use this systematic approach to construct both new and known examples of superactivation of bound entanglement, and examples of activation of BE states using other BE states. A surprising outcome is the construction of noiseless quantum relay channels with no distillable entanglement between any two parties, except for that between the two end nodes.
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An arbitrary amount of entanglement shared among nodes of a quantum network might be nondistillable if the nodes lack the information on the entangled Bell pairs they share. Making such a system distillable, which is called the superactivation of bound entanglement (BE), was shown to be possible through systematic quantum teleportation between the nodes, requiring the implementation of controlled-gates scaling with the number of nodes. In this work, we show in two scenarios that the superactivation of BE is possible if nodes implement the proposed local quantum Zeno strategies based on only single qubit rotations and simple threshold measurements. In the first scenario we consider, we obtain a two-qubit distillable entanglement system as in the original superactivation proposal. In the second scenario, we show that superactivation can be achieved among the entire network of eight qubits in five nodes. In addition to obtaining all-particle distillable entanglement, the overall entanglement of the system in terms of the sum of bipartite cuts is increased. We also design a general algorithm with variable greediness for optimizing the QZD evolution tasks. Implementing our algorithm for the second scenario, we show that a significant improvement can be obtained by driving the initial BE system into a maximally entangled state. We believe our work contributes to quantum technologies from both practical and fundamental perspectives bridging nonlocality, bound entanglement and the quantum Zeno dynamics among a quantum network.
I present a four-party unlockable bound entangled state, that is, a four-party quantum state which cannot be written in a separable form and from which no pure entanglement can be distilled by local quantum operations and classical communication among the parties, and yet when any two of the parties come together in the same laboratory they can perform a measurement which enables the other two parties to create a pure maximally entangled state between them without coming together. This unlocking ability can be viewed in two ways, either as a determination of which Bell state is shared in the mixture or as a kind of quantum teleportation with cancellation of Pauli operators.