Spin swapping operator as an entanglement witness for quantum Heisenberg spin-ssystems
Guang-Ming Zhang, Xiaoguang Wang · Journal of Physics A Mathematical and General · 2006
Using the SU( N ) representation of the group theory, we derive the general form of the spin swapping operator for the quantum Heisenberg spin- s systems. We further prove that such a spin swapping operator is equal to the spin singlet pairing operator under the partial transposition. For SU(2) invariant states, it is shown that the expectation value of the spin swapping operator and its generalizations, the permutations, can be used as an entanglement witness, especially, for the formulation of observable conditions of entanglement.