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

Understand

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.