  Following on from previous work [J. A. Larsson, Phys. Rev. A 67, 022108
(2003)], Bell inequalities based on correlations between binary digits are
considered for a particular entangled state involving 2N trapped ions. These
inequalities involve applying displacement operations to half of the ions and
then measuring correlations between pairs of corresponding bits in the binary
representations of the number of centre-of-mass phonons of N particular ions.
It is shown that the state violates the inequalities and thus displays
nonclassical correlations. It is also demonstrated that it violates a Bell
inequality when the displacements are replaced by squeezing operations.
