Swapping and permutation operators as entanglement witnesses for quantum Heisenberg spin-$s$ systems

Details Swapping and permutation operators as entanglement witnesses for quantum Heisenberg spin-$s$ systems Swapping and permutation operators as entanglement witnesses for quantum Heisenberg spin-$s$ systems

2006-01-19

arxiv.org/abs/quant-ph/0601129v4

J.Phys. A39 (2006) 8515

Physics

Quantum Physics

8 pages, no figures, accepted by Journal of Physics A: Mathematical and General

Scientific paper

10.1088/0305-4470/39/26/017

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.

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