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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Generation and superactivation of bound entanglement

Fumihiro Kaneda, Ryōsuke Shimizu, Satoshi Ishizaka, Yasuyoshi Mitsumori, Hideo Kosaka, Keiichi Edamatsu

Published May 1, 2011• 0 citations
Publisher

Abstract

We report the experimental realization of the four-partite bound-entangled state, i.e., Smolin state and demonstrate the 'superactivation' of the bound entanglement. Bound entanglement is a class of multipartite entanglement that cannot be distilled into pure entanglement under local operations and classical communication (LOCC).

DOI
10.1109/cleoe.2011.5943448

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We report the experimental realization of the four-partite bound-entangled state, i.e., Smolin state and demonstrate the 'superactivation' of the bound entanglement. Bound entanglement is a class of multipartite entanglement that cannot be distilled into pure entanglement under local operations and classical communication (LOCC).
Entanglement is one of the essential resources in quantum information and communication technology (QICT). The entanglement thus far explored and applied to QICT has been pure and distillable entanglement. Yet, there is another type of entanglement, called "bound entanglement," which is not distillable by local operations and classical communication. We demonstrate the experimental "activation" of the bound entanglement held in the four-qubit Smolin state, unleashing its immanent entanglement in distillable form, with the help of auxiliary two-qubit entanglement and local operations and classical communication. We anticipate that it opens the way to a new class of QICT applications that utilize more general classes of entanglement than ever, including bound 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.
A class of unlockable bound entangled states and their applications are presented. They can be considered as quasi generalized Smolin states [Phys. Rev. A 63 (2001) 032306], which are the states of N + N qubits. No pure entanglement can be distilled from this class of states by local quantum operations and classical communications. However, if certain parties group together, they become distillable. Although they are bound entangled states, they could be used to achieve some non-trivial tasks, such as quantum secret sharing shown in the study.
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.