  We use two different approaches to derive multipartite Leggett-type
inequalities, which are generalizations of the two-qubit Leggett-type
inequality obtained in [Nature Phys. \textbf{4}, 681 (2008)]. The first
approach is based on the assumption that the probability distributions should
be non-negative. The second approach is based on a very simple algebraic
equation and is, to some extent, easier than the first approach. Although these
inequalities might not be the optimal ones in the sense that their quantum
violations may not be the strongest, our results make the first step of
generalizing Leggett-type inequality to multi-qubit systems and provide the
possibility to experimentally test non-local realism in such systems. Moreover,
the two approaches here may shed new light on the challenging problem of
obtaining stronger multipartite Leggett-type inequalities.
