A no-go result on common cause approaches via Hardy's paradox

According to a conventional view, there exists no common-cause model of quantum correlations satisfying locality requirements. In fact, Bell's inequality is derived from some locality conditions and the assumption that the common cause exists, and the violation of the inequality has been experimentally verified. On the other hand, some researchers argue that in the derivation of the inequality the existence of a common common-cause for multiple correlations is implicitly assumed and that the assumption is unreasonably strong. According to their idea, what is necessary for explaining the quantum correlation is a common cause for each correlation. However, in this paper, we will show that in almost all entangled states we can not construct a local model that is consistent with quantum mechanical prediction even when we require only the existence of a common cause of each correlation