Abstract

Absolutely Maximally Entangled (AME) states of N quantum systems of dimension d are defined as states that are maximally entangled across an arbitrary non-trivial division into two subsystems, or, equivalently, as states whose reduction to an arbitrary subsystem composed of number of particles not higher than N/2 is maximally mixed. AME sates are a necessary resource in perfect multi-party teleportation and quantum secret sharing, and remain in close relation with many classical and quantum error correction codes. They can be used as a building block in constructing networks exhibiting holographic properties, and, as such, serve as a discrete toy model for quantum gravity. This talk will be devoted to establishing a precise connection between an arbitrary AME stabilizer state and quantum error correction codes emerging from it, as well as providing a description of constructing holographic AME -based networks.