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Chinese Physics B

Entanglement distribution using three-mode separable state with imperfect equipments

Tingting Song, Jie Zhang, Fei Gao, Qiaoyan Wen

Published Jul 1, 2011• 0 citations
Publisher

Abstract

We show a scheme to distribute the entanglement by using three-mode separable Gaussian state prepared with imperfect equipments. The scheme achieves the aim that the entanglement is distributed between two distant parties with only Gaussian operations and linear optics elements. Moreover, we analyse the logarithmic negativity of the entanglement shared between the two parties when the systems are imperfect and arrive at the conclusion that the logarithmic negativity is asymptotically stable with fluctuations within a certain space range.

DOI
10.1088/1674-1056/20/7/070306

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We show a scheme to distribute the entanglement by using three-mode separable Gaussian state prepared with imperfect equipments. The scheme achieves the aim that the entanglement is distributed between two distant parties with only Gaussian operations and linear optics elements. Moreover, we analyse the logarithmic negativity of the entanglement shared between the two parties when the systems are imperfect and arrive at the conclusion that the logarithmic negativity is asymptotically stable with fluctuations within a certain space range.
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We propose an entanglement sharing protocol based on separable states. Initially, two parties, Alice and Bob, share a two-mode separable Gaussian state. Alice then splits her mode into two separable modes and distributes them between two players. Bob is separable from the players but he can create entanglement with either of the players if the other player moves to his location and collaborates with him. Any two parties are separable and the creation of entanglement is thus mediated by transmission of a mode which is separable from individual modes on Alice's side and Bob's side. For the state shared by the players and Bob one cannot establish entanglement between any two modes even with the help of operation on the third mode provided that Bob is restricted to Gaussian measurements and the state thus carries a nontrivial signature of bound entanglement. The present protocol also demonstrates switching between different separability classes of tripartite systems by coherent operations on its bipartite parts and complements studies on protocols utilizing mixed partially entangled multipartite states.
We investigate the physical mechanism behind the counterintuitive phenomenon, the distribution of continuous-variable entanglement between two distant modes by sending a third separable auxiliary mode between them. For this purpose, we propose a more simple and more efficient protocol resulting in distributed entanglement with more than an order of the magnitude higher logarithmic negativity than in the previously proposed protocol. This protocol shows that the distributed entanglement originates from the entanglement of one mode and the auxiliary mode used for distribution, which is first destroyed by local correlated noises and restored subsequently by the interference of the auxiliary mode with the second distant separable correlated mode.
We show that three distant parties, AAA, BBB, and CCC, having no prior entanglement can establish a shared GHZ state by mediating two particles which remain separable from each other and from all the other parties throughout the process. The success probability is 1/71/71/7. We prove this in a general framework for systematic distribution of entangled states between two and more parties with separable states in ddd dimensions. The proposed method may facilitate the construction of multinode quantum networks and many other processes which use multipartite entangled states.
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Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography, and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure that is straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.