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arXiv:quant-ph/0005117 · Physical Review Letters

Superactivation of Bound Entanglement

Peter W. Shor, John A. Smolin, Ashish V. Thapliyal

Published Mar 10, 2003• 111 citations
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Abstract

We show that, in a multiparty setting, two nondistillable (bound-entangled) states tensored together can make a distillable state. This is an example of true superadditivity of distillable entanglement. We also show that unlockable bound-entangled states cannot be asymptotically unentangled, providing the first proof that some states are truly bound-entangled in the sense of being both nondistillable and nonseparable asymptotically.

DOI
10.1103/physrevlett.90.107901

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We show that, in a multiparty setting, two nondistillable (bound-entangled) states tensored together can make a distillable state. This is an example of true superadditivity of distillable entanglement. We also show that unlockable bound-entangled states cannot be asymptotically unentangled, providing the first proof that some states are truly bound-entangled in the sense of being both nondistillable and nonseparable asymptotically.
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.
We study the relation between violation of Bell inequalities and distillability properties of quantum states. Recently, Dür [Phys. Rev. Lett. 87, 230402 (2001)] has shown that there are some multiparticle bound entangled states which are nonseparable and nondistillable, that violate a Bell inequality. We prove that for all the states violating this inequality there exists at least one splitting of the parties into two groups such that some pure-state entanglement can be distilled, obtaining a connection between Bell inequalities and bipartite distillable entanglement.
The superactivation of multipartite bound entanglement (BE) is a special protocol proposed by Shor et al. in 2003, which can distill Einstein-Podolsky-Rosen (EPR) entanglement states between two subsystems of two multipartite BE states. Here we present the first experimental realization of the superactivation of the BE state, in which two copies of the four-partite unlockable BE state in a continuous-variable regime are used. Coupling two thermal states with Gaussian noises into two submodes of an EPR entangled state on two 50-50 beam splitters respectively, the four output optical modes form a four-partite unlocklable BE state. Using two EPR entangled states, we experimentally produce two BE states first. Then through a superactivation operation involving measurements and feedback on the two BE states, an EPR entangled state is distilled out between two designated parties of the two four-partite BE states. The experiment demonstrates the superadditivity of quantum entanglement as the individual BE state cannot be distilled, only two BE states together can be distilled.