  Our work addresses the problem of generating maximally entangled two spin-1/2
(qubit) symmetric states using NMR, NQR, Lipkin-Meshkov-Glick Hamiltonians.
Time evolution of such Hamiltonians provides various logic gates which can be
used for quantum processing tasks. Pairs of spin-1/2's have modeled a wide
range of problems in physics. Here we are interested in two spin-1/2 symmetric
states which belong to a subspace spanned by the angular momentum basis {|j =
1, {\mu}>; {\mu} = +1, 0,-1}. Our technique relies on the decomposition of a
Hamiltonian in terms of SU(3) generators. In this context, we define a set of
linearly independent, traceless, Hermitian operators which provides an
alternate set of SU(n) generators. These matrices are constructed out of
angular momentum operators Jx,Jy,Jz. We construct and study the properties of
perfect entanglers acting on a symmetric subspace i.e., spin-1 operators that
can generate maximally entangled states from some suitably chosen initial
separable states in terms of their entangling power.
