真正纠缠的子空间和四体系统中强非局域的不可扩展双分离基
Genuinely entangled subspaces and strongly nonlocal unextendible biseparable bases in four-partite systems
AI总结：
本文研究四量子比特系统中真正纠缠子空间的构建，证明其强非局域性并展示其在所有双分拆上的可蒸馏性，为量子信息处理提供理论基础。
摘要：
一组正交的纯态被称为不可扩展双分离基（UBB），这意味着其互补子空间仅包含真正纠缠态。UBB因此成为构建真正纠缠子空间的有效工具。如果此类子空间中的每一个态在所有双分拆上都表现出可蒸馏的纠缠性，它将特别有利于量子信息应用。在本文中，我们主要研究四量子比特系统，其中局部维度d不少于3。我们提出了一种构建UBB的方法，并证明通过这种方式建立的UBB是强非局域的。我们构建了几个真正纠缠的子空间，并展示了在所有双分拆上真正纠缠子空间的可蒸馏性。此外，我们还描述了某些真正纠缠子空间的特定正交基。这些结果不仅有助于量子非局域性理论的发展，还为实际的量子信息处理任务提供了关键的理论基础。
英文摘要：
A set of orthogonal pure states is an unextendible biseparable basis (UBB), which means that its complementary subspace contains only genuinely entangled states. UBBs thus serve as an effective tool for constructing genuinely entangled subspaces. If every state within such a subspace exhibits distillable entanglement across all bipartitions, it becomes particularly advantageous for applications in quantum information. In this paper, we mainly conduct research on the 4-qudit quantum systems, where the local dimension $d$ is not less than 3. We present an approach for constructing UBB and prove that the UBB established in this way is strongly nonlocal. We build several genuinely entangled subspaces and demonstrate the distillability of the genuinely entangled subspaces across all bipartitions. In addition, we also describe the specific orthonormal basis for some genuinely entangled subspaces. These results will not only contribute to the development of quantum nonlocality theory, but also provide a crucial theoretical foundation for practical quantum information processing tasks.
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