Exchange Symmetry and Multipartite Entanglement

Details Exchange Symmetry and Multipartite Entanglement Exchange Symmetry and Multipartite Entanglement

2008-05-23

arxiv.org/abs/0805.3625v3

Phys. Rev. A78 (2008) 052105

Physics

Quantum Physics

12 pages, appendix added

Scientific paper

10.1103/PhysRevA.78.052105

Entanglement of multipartite systems is studied based on exchange symmetry under the permutation group S_N. With the observation that symmetric property under the exchange of two constituent states and their separability are intimately linked, we show that anti-symmetric (fermionic) states are necessarily globally entangled, while symmetric (bosonic) states are either globally entangled or fully separable and possess essentially identical states in all the constituent systems. It is also shown that there cannot exist a fully separable state which is orthogonal to all symmetric states, and that full separability of states does not survive under total symmetrization unless the states are originally symmetric. Besides, anyonic states permitted under the braid group B_N should also be globally entangled. Our results reveal that exchange symmetry is actually sufficient for pure states to become globally entangled or fully separable.

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