Table of AME states

Table on the existence of absolutely maximally entangled states (AME) of n parties with D levels each.
Abbreviated as AME(n,D), these states are equivalent to pure ((n,1,n/2+1))_D quantum error correcting codes.
In the case of n even they are also known as perfect tensors or multi-unitary matrices.

Last updated: 22.02.2024
Number of parties n
Name:
 
Exists:
 
Constructions:
 
Comments:
 
References:
 
Abbreviations:

     exists       non-existing       non-existing, excluded by Shadow       non-existing, excluded by Scott bound

Stab: stabilizer states
OA: orthogonal arrays construction
CMDS/MS: originate from classical minimal distance separable codes, equivalent to AME states of minimal support, and related to orthogonal arrays of index unity.