Quantum error correction codes and absolutely maximally entangled states

Understand

For every stabiliser $N$-qudit absolutely maximally entangled state, we present a method for determining the stabiliser generators and logical operators of a corresponding quantum error correction code.

• These codes encode $k$ qudits into $N-k$ qudits, with $k\leq \left \lfloor{N/2} \right \rfloor$, where the local dimension $d$ is prime.
• We use these methods to analyse 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.