Average correlation as an indicator for inseparability

Inseparability of quantum states is one of the most crucial aspects of quantum physics, as it often provides the key ingredient for obtaining a quantum advantage. Quantifying inseparability is thus an important objective to better understand quantum physics and to improve quantum applications. So far, many measures for inseparability exist, however, most of them are based on abstract mathematical procedures and are not defined operationally which can easily be realized in an experiment. Recently we introduced average correlation [Tschaffon et al., Phys. Rev. Res. 5, 023063 (2023)] as a reference frame independent indicator for nonclassicality in the Bell sense based on randomized measurements. It is defined as the average absolute value of the two-qubit correlation function and allows one to formulate a necessary and sufficient condition for the ability to violate the CHSH inequality. Experimentally it can be realized by randomized measurements which can approximate its value arbitrarily closely. This makes it independent of a shared reference frame between the two measuring parties, which can be useful in scenarios where it is impossible to find one. In this second article, we show that average correlation also serves as an indicator for inseparability by deriving a necessary and sufficient condition. From there, we prove the remaining open conjectures of the first article. Due to the operational definition of average correlation, it offers a first step toward finding a new operationally defined inseparability measure.