We study the holographic complexity of Einstein-Maxwell-Dilaton gravity using the recently proposed "complexity = volume" and "complexity = action" dualities. The model we consider has a ground state that is represented in the bulk via a so-called hyperscaling violating geometry. We calculate the action growth of the Wheeler-DeWitt patch of the corresponding black hole solution at non-zero temperature and find that, in the presence of violations of hyperscaling, there is a parametric enhancement of the action growth rate. We partially match this behavior to simple tensor network models which can capture aspects of hyperscaling violation. We also exhibit the switchback effect in complexity growth using shockwave geometries and comment on a subtlety of our action calculations when the metric is discontinuous at a null surface.

1 aSwingle, Brian1 aWang, Yixu uhttps://arxiv.org/abs/1712.0982601111nas a2200109 4500008004100000245004900041210004900090520079100139100001900930700001500949856003700964 2018 eng d00aRecovery Map for Fermionic Gaussian Channels0 aRecovery Map for Fermionic Gaussian Channels3 aA recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. We also discuss subtleties arising from the singularities of the involved matrices.

1 aSwingle, Brian1 aWang, Yixu uhttps://arxiv.org/abs/1811.04956