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Physical Review Letters

Superactivation of Multipartite Unlockable Bound Entanglement

Xiaojun Jia, Jing Zhang, Yu Wang, Yaping Zhao, Changde Xie, Kunchi Peng

Published May 9, 2012• 22 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.108.190501

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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.
In quantum networks, after passing through noisy channels or information processing, residual states may lack sufficient entanglement for further tasks, yet they may retain hidden quantum resources that can be recycled. Efficiently recycling these states to extract entanglement resources, such as genuine multipartite entanglement or Einstein-Podolsky-Rosen pairs, is essential for optimizing network performance. Here, we develop a tripartite entanglement distillation scheme using an eight-photon quantum platform, demonstrating entanglement superactivation phenomena which are unique to multipartite systems. We successfully generate a three-photon genuinely entangled state from two biseparable states via local operations and classical communication, demonstrating superactivation of genuine multipartite entanglement. Furthermore, we extend our scheme to generate a three-photon state capable of extracting an Einstein-Podolsky-Rosen pair from two initial states lacking this capability, revealing a previously unobserved entanglement superactivation phenomenon. Our methods and findings offer not only practical applications for quantum networks, but also lead to a deeper understanding of multipartite entanglement structures.
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.
Quantum entanglement shared by more than two partites is the essential bases for developing quantum communication networks and quantum computation. The multipartite entanglement of continuous variables can be generated by distributing or combining squeezed states of light using linear optics. We experimentally obtained a tripartite entangled state of bright optical field by means of a nondegenerate optical parametric amplifier (NOPA) and optical beam-splitters. The NOPA is operated in the state of parametric deamplification by locking the relative phase between the pump laser and the injected seed wave to (2n+1)π, so the generated Einstein-Podolsky-Rosen (EPR) beam for continuous variables is an entangled state of light with the quantum correlation of phase quadratures and the quantum anticorrelation of amplitude quadratures [1]. The output EPR beam consists of two frequency-degenerate optical modes with horizontal and vertical polarizations which are distributed to three parties with two linear beam-splitters. We have theoretically and experimentally demonstrated the three parties are in a tripartite entangled state with three-mode “position” (amplitude quadrature) correlation and relative “momentum” (phase quadrature) correlation [2]-[4]. The obtained GHZ-like state is a fully inseparable tripartite continuous-variables state violating the three inequalities used for the criterion of the inseparability [5][6]. The controlled dense coding quantum communication is experimentally accomplished by exploiting the tripartite entanglement. The three entangled modes are sent to a sender (Alice), a receiver (Bob) and a controller (Claire), respectively. The information transmission capacity of the quantum channel between Alice and Bob is controlled by Claire. The channel capacity completed under Claire’s help is always larger than that without her help.
Bound information, a cryptographic classical analog of bound entanglement, is defined as classical secret correlations from which no secret key can be extracted. Its existence was conjectured and shown in a multipartite case. In this work, we provide an example of bound information in a four-partite scenario. Later, using this example, we prove that bound information can be superactivated and moreover unlockable in a finite-copy scenario. We also show that bound entangled states (bound information) can be used to distribute multipartite pure-state entanglements (secret keys).