Coherence and entropy complementarity relations of generalized wave-particle duality

Abstract: The concept of wave-particle duality holds significant importance in the field of quantum mechanics, as it elucidates the dual nature encompassing both wave-like and particle-like properties exhibited by microscopic particles. In this paper, we construct generalized measures for the predictability and visibility of $n$-path interference fringes to quantify the wave and particle properties in quantum high-dimensional systems. By employing the Morozova-Chentsov function, we ascertain that the wave-particle relationship can be delineated by the average coherence. This function exhibits a close correlation with the metric-adjusted skew information, thereby we establish complementary relations between visibility, predictability, and quantum $f$ entropy, which reveals deep connections between wave-particle duality and other physical quantities. Through our methodology, diverse functions can be selected to yield corresponding complementary relationships.