Relating Entanglement and Nonlocality

Abstract

Both entanglement and nonlocality are central concepts in modern physics. Their relation, however, is not fully understood yet. In 1964, Bell showed that some entangled states are nonlocal, in the sense that the statistics obtained when certain measurements are performed on them would violate a Bell inequality (Bell, Physics, 1:195–200, 1964, [Bel64]). In 1991, Gisin showed that every pure bipartite entangled state is nonlocal (Gisin, Phys Lett A 154:201–202, 1991, [Gis91]), a result that was later generalized to any multipartite pure entangled quantum state a bit later by Popescu and Rohrlich (Phys Lett A 166:293–297, 1992, [PR92]). Thus, one could naively identify nonlocality and entanglement, however, this intuition is—like in many situations in quantum physics—misleading, as the relation between those two quantum information resources is more involved.