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We consider a class of holographic quantum errorcorrecting codes, built from perfect tensors in network configurations dual to BruhatTits trees and their quotients by Schottky groups corresponding to BTZ black holes. The resulting holographic states can be constructed in the limit of infinite network size. We obtain a padic version of entropy which obeys a RyuTakayanagi like formula for bipartite entanglement of connected or disconnected regions, in both genuszero and genusone padic backgrounds, along with a BekensteinHawkingtype formula for black hole entropy. We prove entropy inequalities obeyed by such tensor networks, such as subadditivity, strong subadditivity, and monogamy of mutual information (which is always saturated). In addition, we construct infinite classes of perfect tensors directly from semiclassical states in phase spaces over finite fields, generalizing the CRSS algorithm, and give Hamiltonians exhibiting these as vacua.
https://arxiv.org/pdf/1812.04057.pdf
https://www.mpimbonn.mpg.de/node/7193
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