Maximally entangled unitary operators have been of prime focus in many-body
physics, quantum information, and black-hole physics in recent past. Bipartite maximally entangled unitary operators dubbed as “dual-unitary” operators are used as building blocks of
solvable models of many-body quantum chaos. Maximally entangling bipartite unitary operators called as “2-unitary operators” or “perfect tensors” are maximally entangled unitary operators which satisfy additional constraints and are used to construct absolutely maximally entangled
(AME) states of four qudits. AME states are genuinely multipartite entangled states; subsytems
along any balanced bipartition are maximally mixed, which are very useful in constructing quantum error correcting codes. In this work we discuss one of the open problem in quantum information about the existence of AME(4, 6); AME state of four qudits where dimension of each qudit
is 6, or equivalently, 2-unitary of order 36 or perfect tensor with 4 indices or legs each running
from 0 to 5. We propose a way to extend the concept of dual-unitarity to bipartite unitary operators which act on systems with different local Hibert dimension and to multipartite systems
as well. Constructions of maximally entangled and maximally entangling unitary operators in
these cases using non-linear dynamical maps defined on the space of unitary operators are briefly
discussed.