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

## TL;DR

This paper explores the connection between absolutely maximally entangled states and quantum maximum distance separable codes, demonstrating how AME states can generate QMDS codes useful for efficient quantum repeaters.

## Contribution

It introduces a new stabilizer form for AME states, enabling the construction of QMDS codes and their application in optimizing quantum repeater infrastructure.

## Key findings

- Constructed families of QMDS codes from AME states.
- Related AME-based codes to quantum repeater cost optimization.
- Provided a stabilizer framework for AME states and derived codes.

## Abstract

We extend the relation between absolutely maximally entangled (AME) states and quantum maximum distance separable (QMDS) codes by constructing whole families of QMDS codes from their parent AME states. We introduce a 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. 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. We establish that AME states provide a framework for a class of QMDS codes that can be used in quantum repeaters.