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We consider violations of a Clauser-Horne-Shimony-Holt-type steeringinequality for quantum states of systems of indistinguishable particlesrestricted by a particle-number-superselection rule. We check for violations innon-interacting Bose-Einstein condensate and N00N states, by using two copiesof the states for bypassing the superselection rule. The superselection ruleprevents the states from maximally violating the steering inequality. But thesteering inequality violations are higher than Bell inequality violations forthe same states. This in particular implies, in certain cases, thatvisibilities of the steering inequality violations are higher than the same forBell inequality violations, for admixtures with white noise. We also found thatan increase in the number of particles in the non-interacting condensate statesresults in a decrease of the violation amount of the steering inequality.

Steering inequality for pairs of particle-number-superselection-rule restricted states