Constructions of k-uniform and absolutely maximally entangled states beyond maximum distance codes

TL;DR

This paper introduces a new systematic method for constructing k-uniform and absolutely maximally entangled states, expanding beyond traditional maximum distance separable codes and solving open existence questions.

Contribution

The authors develop a novel construction approach for k-uniform and absolutely maximally entangled states that are not derived from classical error correction codes.

Findings

Constructed new classes of k-uniform states beyond MDS codes

Generated examples of previously unknown absolutely maximally entangled states

Demonstrated the non-equivalence of new states to existing code-based states

Abstract

Pure multipartite quantum states of n parties and local dimension q are called k-uniform if all reductions to k parties are maximally mixed. These states are relevant for our understanding of multipartite entanglement, quantum information protocols, and the construction of quantum error correction codes. To our knowledge, the only known systematic construction of these quantum states is based on classical error correction codes. We present a systematic method to construct other examples of k-uniform states and show that the states derived through our construction are not equivalent to any k-uniform state constructed from the so-called maximum distance separable error correction codes. Furthermore, we use our method to construct several examples of absolutely maximally entangled states whose existence was open so far.