Absolutely maximally entangled states, quantum-maximum-distance-separable codes, and quantum repeaters

We address the relation between absolutely maximally entangled (AME) states and quantum- maximum-distance-separable (QMDS) codes by constructing whole families of QMDS codes from AME states that have stabilizer representations. We introduce a generic reduction-friendly form for the generator set of the stabilizer representation of an AME state, from which the stabilizer form for children codes, all QMDS, can be obtained. Our method would work for relevant high-dimensional codes as well as qubit-based codes. We then relate this to optimal codes for one-way quantum repeaters, by minimizing the short-term infrastructure cost as well as the long-term running cost of such quantum repeaters. This would allow us to obtain the optimal QMDS code, derived from an AME parent state, that can be used in such quantum repeaters.

Automated summary

The paper explores the relationship between AME states and QMDS codes by constructing QMDS codes from AME states with stabilizer representations. A reduction-friendly form for the generator set of stabilizer representation of an AME state is introduced, from which stabilizer form for children codes, all QMDS, can be obtained. The method is applicable to high-dimensional codes as well as qubit-based codes, and can be used to derive optimal QMDS codes for one-way quantum repeaters.