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Holographic study of entanglement and complexity for mixed states

机译：混合状态纠缠与复杂性的全息研究

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In this paper, we holographically quantify the entanglement and complexity for mixed states by following the prescription of purification. The bulk theory we consider in this work is a hyperscaling violating solution, characterized by two parameters, hyperscaling violating exponent θ and dynamical exponent z . This?geometry is due to a nonrelativistic strongly coupled theory with hidden Fermi surfaces. We first compute the holographic analogy of entanglement of purification, denoted as the minimal area of the entanglement wedge cross section and observe the effects of z and θ . Then in order to probe the mixed state complexity we compute the mutual complexity for the Banados Teitelboim Zanelli (BTZ) black hole and the hyperscaling violating geometry by incorporating the holographic subregion complexity conjecture. We carry this out for two disjoint subsystems separated by a distance and also when the subsystems are adjacent with subsystems making up the full system. Furthermore, various aspects of holographic entanglement entropy such as the entanglement Smarr relation, the Fisher information metric, and the butterfly velocity have also been discussed.
机译：在本文中，我们通过遵循纯化处方时，全拍方式量化混合状态的缠结和复杂性。我们考虑在这项工作中的批量理论是一个超高度的违规解决方案，其特征在于两个参数，超出违反指数θ和动态指数z。这个？几何形状是由于隐藏的费米表面的非椭圆强烈耦合理论。首先，首先计算纯化缠结的全息图谱，表示为纠缠楔形横截面的最小面积，观察Z和θ的效果。然后为了探测混合状态复杂性，通过结合全息子区域复杂性猜想来计算BANADOS TEITELBOIM ZANELLI（BTZ）黑洞的相互复杂性和违反几何形状。我们为两个差分子系统携带这一点，并且当子系统与构成完整系统的子系统相邻时。此外，还讨论了全息缠结熵的各个方面，例如纠缠Smarr关系，Fisher信息度量和蝶形速度。

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