Generalizations of the pseudospin operator to test the Bell inequality for the TMSV state

Chen et al (2002 Phys. Rev. Lett. 88 040406) proposed a method to measure the entanglement of a bipartite quantum system involving continuous variables. The approach is based upon the construction of a pseudospin operator. An important difference with the spin case is an infinite degeneracy of the eigenkets associated with the pseudospin. In this paper, we analyze the role played by such a degeneracy in the study of the locality of the two-mode-squeezed vacuum state. We construct other representations for the pseudospin and study the corresponding Bell inequalities.