General framework of quantum complementarity from a measurement-based perspective

One of the most remarkable features of quantum physics is that attributes of quantum objects, such as the wave-like and particle-like behaviors of single photons, can be complementary in the sense that they are equally real but cannot be observed simultaneously. Quantum measurements, serving as windows providing views into the abstract edifice of quantum theory, are basic tools for manifesting the intrinsic behaviors of quantum objects. However, quantitative formulation of complementarity that highlights its manifestations in sophisticated measurements remains elusive. Here we develop a general framework for demonstrating quantum complementarity in the form of information exclusion relations (IERs), which incorporates the wave-particle duality relations as particular examples. Moreover, we explore the applications of our theory in entanglement witnessing and elucidate that our IERs lead to an extended form of entropic uncertainty relations, providing intriguing insights into the connection between quantum complementarity and the preparation uncertainty.