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arXiv 1406.2663hep-thgr-qcquant-ph
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多边界虫洞与全息纠缠

Multiboundary Wormholes and Holographic Entanglement

Vijay Balasubramanian, Patrick Hayden, Alexander Maloney, Donald Marolf, Simon F. Ross

备注：
64 pages; v2: Improved argument for large L_3 limit
发表信息：
Classical and Quantum Gravity, 31(18):185015, 2014
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摘要：

AdS/CFT对应关系将边界共形场论与对偶渐近Anti-de Sitter时空中的几何联系之间的量子纠缠联系起来。我们考虑1+1维CFT Hilbert空间的n重张量积中的纠缠态，该空间由具有n个孔的Riemann表面上的欧几里得路径积分定义。在模空间的一个区域中，对偶体态是一个黑洞，n个渐近AdS_3区域由一个共同的虫洞连接，而在其他区域中的块分裂成不连接的组件。我们研究了纠缠结构，并利用CFT n点函数计算了黎曼面穿刺极限下的波函数。我们还使用AdS最小曲面来更普遍地测量纠缠。在某些区域的模空间的纠缠是完全多部的，虽然不是GHZ型。然而，即使当块体完全连接时，在模空间的某些区域中，纠缠几乎完全是二分的：仅在成对的CFTs之间发生显著的纠缠。我们开发了新的工具来分析内在的n-体纠缠，并使用这些来表明，对于一些虫洞与n个类似大小的视野有至少n-1方之间的内在纠缠，并在渐近区域之间的纠缠至少是（n+1）/2 particulate。

英文摘要：

The AdS/CFT correspondence relates quantum entanglement between boundary Conformal Field Theories and geometric connections in the dual asymptotically Anti-de Sitter space-time. We consider entangled states in the n-fold tensor product of a 1+1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk state is a black hole with n asymptotically AdS_3 regions connected by a common wormhole, while in other regions the bulk fragments into disconnected components. We study the entanglement structure and compute the wave function explicitly in the puncture limit of the Riemann surface in terms of CFT n-point functions. We also use AdS minimal surfaces to measure entanglement more generally. In some regions of the moduli space the entanglement is entirely multipartite, though not of the GHZ type. However, even when the bulk is completely connected, in some regions of the moduli space the entanglement is almost entirely bipartite: significant entanglement occurs only between pairs of CFTs. We develop new tools to analyze intrinsically n-partite entanglement, and use these to show that for some wormholes with n similar sized horizons there is intrinsic entanglement between at least n-1 parties, and that the distillable entanglement between the asymptotic regions is at least (n+1)/2 partite.

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