  Causal inequalities are bounds on correlations obtained when operations take
place in a causal sequence, i.e. in which the background time or definite
causal structure pre-exists such that every operation is either in the future,
in the past or space-like separated from any other operation. Recently, a
framework was developed where quantum theory is assumed to be valid in local
laboratories, but where no reference is made to any global causal relations
between the operations in the laboratories. The framework was shown to allow
for correlations that violate a bipartite causal inequality. Here we prove that
the maximal violation of the causal inequality is upper bounded (analogously to
the "Tsirelson bound") under a restricted set of local operations involving
traceless binary observables. The bound is lower than what is algebraically
possible.
