  Realignment operation has a significant role in detecting bound as well as
free entanglement. Just like partial transposition, it is also based on
permutations of the matrix elements. However, the physical implementation of
realignment operation is not known yet. In this letter, we address the problem
of experimental realization of realignment operation and to achieve this aim,
we propose a theoretical proposal for the same. We first show that after
applying the realignment operation on a bipartite state, the resulting matrix
can be expressed in terms of the partial transposition operation along with
column interchange operations. We observed that these column interchange
operations forms a permutation matrix which can be implemented via SWAP
operator acting on the density matrix. This mathematical framework is used to
exactly determine the first moment of the realignment matrix experimentally.
This has been done by showing that the first moment of the realignment matrix
can be expressed as the expectation value of a SWAP operator which indicates
the possibility of its measurement. Further, we have provided an estimation of
the higher order realigned moments in terms of the first realigned moment and
thus pave a way to estimate the higher order moments experimentally. Next, we
develop moments based entanglement detection criteria that detect positive
partial transpose entangled states (PPTES) as well as negative partial
transpose entangled states (NPTES). Moreover, we define a new matrix
realignment operation for three-qubit states and have devised an entanglement
criteria that is able to detect three-qubit fully entangled states. We have
developed various methods and techniques in the detection of bipartite and
tripartite entangled states that may be realized in the current technology.
