Absolutely maximally entangled state

The absolutely maximally entangled (AME) state is a concept in quantum information science, which has many applications in quantum error-correcting code, discrete AdS/CFT correspondence, and AdS/CMT correspondence, etc.

Definition

The bipartite maximally entangled states $|\psi \rangle _{AB}$ is the one that the reduced density operators are maximally mixed, i.e., $\rho _{A}=\rho _{B}=I/d$. Typical examples are Bell states.

A multipartite state $|\psi \rangle$ of a system $S$ is called called absolutely maximally entangled if for any bipartition $A|B$ of $S$, the reduced density operator is maximally mixed $\rho _{A}=\rho _{B}=I/d$, where $d=\min\{d_{A},d_{B}\}$.

Property

The AME state does not always exit, in some give local dimension and number of party, there is no AME state. For a table of AME state in low dimensions, see table of AME states.