Quantum error-correction codes and absolutely maximally entangled states

For every stabilizer N-qudit absolutely maximally entangled state, we present a method for determining the stabilizer generators and logical operators of a corresponding quantum error-correction code. These codes encode k qudits into N - k qudits, with k <= left perpendicular N/2 right perpendicular, where the local dimension d is prime. We use these methods to analyze the concatenation of such quantum codes and link this procedure to entanglement swapping. Using our techniques, we investigate the spread of quantum information on a tensor network code formerly used as a toy model for the AdS/CFT correspondence. In this network, we show how corrections arise to the Ryu-Takayanagi formula in the case of entangled input state, and that the bound on the entanglement entropy of the boundary state is saturated for absolutely maximally entangled input states.