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Science Advisor

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**Classical Holographic Codes**

Enrico M. Brehm, Benedikt Richter

(Submitted on 12 Sep 2016)

In this work, we introduce classical holographic codes. These can be understood as concatenated probabilistic codes and can be represented as networks uniformly covering hyperbolic space. In particular, classical holographic codes can be interpreted as maps from bulk degrees of freedom to boundary degrees of freedom. Interestingly, they are shown to exhibit features similar to those expected from the AdS/CFT correspondence. Among these are a version of the Ryu-Takayanagi formula and intriguing properties regarding bulk reconstruction and boundary representations of bulk operations. We discuss the relation of our findings with expectations from AdS/CFT and, in particular, with recent results from quantum error correction.

http://arxiv.org/abs/1609.03651

**Discussion of the Entanglement Entropy in Quantum Gravity**

Chen-Te Ma

(Submitted on 13 Sep 2016)

Quantum gravity needs to be satisfied by the holographic principle, and the entanglement entropy already has holographic evidences via anti-de Sitter/ Conformal field theory correspondence. Thus, we explore principles of quantum gravity via the entanglement entropy. We compute the entanglement entropy in two dimensional Einstein-Hilbert action to understand quantum geometry and area law. Then we also discuss two dimensional conformal field theory because we expect strongly coupled conformal field theory can describe perturbative quantum gravity theory. We find universal terms of the entanglement entropy is independent of a choice of an entangling surface in two dimensional conformal field theory for one interval and some cases of multiple intervals. To extend our discussion to generic multiple intervals, we use a geometric method to determine the entanglement entropy. Finally, we argue translational invariance possibly be a necessary condition in quantum gravity theory from ruing out volume law of the entanglement entropy.

http://arxiv.org/abs/1609.03991

**Entwinement in discretely gauged theories**

V. Balasubramanian, A. Bernamonti, B. Craps, T. De Jonckheere, F. Galli

(Submitted on 13 Sep 2016)

We develop the notion of entwinement to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an ##S_{N}## gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to ##AdS_{3}## at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the system which are gravitationally described as conical defects and the M=0 BTZ black hole. The possible types of entwinement that can be computed define a very large new class of quantities characterizing the fine structure of quantum wavefunctions.