Reichenbach’s common cause completeness in symmetric-difference-closed quantum logics

Abstract One of the lines of recent quantum logic investigations concern the quantum logics that are endowed with an operation of symmetric difference (with a XOR operation). It is natural to ask whether these logics might be relevant to the study of Reichenbach’s common cause principle (RCCP). The principle states that any two positively correlated events allow for a common cause. In the mathematical formulation, one asks if there are symmetric-difference-closed (non-Boolean) quantum logics that enable a positive answer as regards the RCCP. In this note we show that there are such logics.