Quantum violations of joint reality

Based on (i) the physical principle of local causality and (ii) a certain notion of elements of reality, Einstein, Podolsky, and Rosen put forward an argument showing that physical instances may exist in which two noncommuting observables can be joint elements of the physical reality. Here, we introduce a new criterion of joint reality. We demonstrate that according to this criterion, quantum mechanics generally prevents noncommuting observables from having joint elements of reality. In addition, we introduce a measure to quantify the extent to which the criterion is violated and explore the implications of such a measure in connection with incompatibility and correlations. Our findings suggest new manners of interpreting quantum phenomena.