Investigation of absolutely maximally entangled states: A maximum concurrence criterion

We introduce a method to determine the maximal entanglement of pure states using the concept of I-concurrence, a measure of entanglement. For a bipartition X/X^' of a pure state, the squared concurrence is expressed as E²_X/X^'=2[1−tr(ρ²_X)] having the maximum value when tr(ρ²_X) will be minimum. Using this approach, we have identified all possible pure Absolutely Maximally Entangled (AME) states for some qubit cases showing maximal entanglement across all possible bipartitions. We have also shown that pure states with an odd number of subsystem coefficients do not meet the AME criterion. Again, we have discussed equal maximal multipartite entangled pure states using our approach.