Multipartite Einstein-Podolsky-Rosen (EPR) steering admits multipartite entanglement in the presence of uncharacterized verifiers, enabling practical applications in semi-device-independent protocols. Such applications generally require stronger steerability, while the unavoidable noise weakens steerability and consequently degrades the performance of quantum information processing. Here, we propose the local filtering operation that can maximally distill genuine tripartite EPR steering from N$N$ copies of three-qubit generalized Greenberger-Horne-Zeilinger states, in the context of two semi-device-independent scenarios. The optimal filtering operation is determined by the maximization of assemblage fidelity. Analytical and numerical results indicate the advantage of the proposed filtering operation when N$N$ is finite and the steerability of initial assemblages is weak. Experimentally, a proof-of-principle demonstration of two-copy distillation is realized with the optical system. The advantage of the optimal local filtering operation is confirmed by the distilled assemblage in terms of higher assemblage fidelity with perfectly genuine tripartite steerable assemblages, as well as the greater violation of the inequality to witness genuine tripartite steerable assemblages. Our results benefit the distillation of multipartite EPR steering in practice, where the number of copies of initial assemblages is generally finite.

中文翻译：

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具有最佳局部滤波操作的三方量子操纵的实验蒸馏

多方爱因斯坦-波多尔斯基-罗森（EPR）控制在存在未表征的验证者的情况下承认多方纠缠，从而在半设备无关协议中实现实际应用。此类应用通常需要更强的可操纵性，而不可避免的噪声会削弱可操纵性，从而降低量子信息处理的性能。在这里，我们提出了局部过滤操作，可以在两个半设备独立场景的背景下，从三量子位广义 Greenberger-Horne-Zeilinger 状态的 N 个副本中最大限度$N$地提取真正的三方 EPR 转向。最佳过滤操作由组合保真度的最大化来确定。分析和数值结果表明，当N$N$有限且初始组合的可操纵性较弱时，所提出的滤波操作具有优势。在实验上，通过光学系统实现了两份蒸馏的原理验证演示。最佳局部滤波操作的优点通过蒸馏组合得到了证实，即具有完全真实的三方可操纵组合的更高的组合保真度，以及对见证真正的三方可操纵组合的不等式的更大破坏。我们的结果有利于实践中多部分 EPR 控制的提炼，其中初始组合的副本数量通常是有限的。