  We consider violations of a Clauser-Horne-Shimony-Holt-type steering
inequality for quantum states of systems of indistinguishable particles
restricted by a particle-number-superselection rule. We check for violations in
non-interacting Bose-Einstein condensate and N00N states, by using two copies
of the states for bypassing the superselection rule. The superselection rule
prevents the states from maximally violating the steering inequality. But the
steering inequality violations are higher than Bell inequality violations for
the same states. This in particular implies, in certain cases, that
visibilities of the steering inequality violations are higher than the same for
Bell inequality violations, for admixtures with white noise. We also found that
an increase in the number of particles in the non-interacting condensate states
results in a decrease of the violation amount of the steering inequality.

Quantum Physics