Wave‐Particle‐Mixedness Relationships Based on <i>l</i> _<i>p</i> ‐norm Coherence

ABSTRACT We investigate the relationships among the wave property, particle property and mixedness of quantum states based on the ‐norm coherence. By conforming that the ‐norm coherence is an appropriate measure of wave property and introducing a measure of particle property based on the differences between the maximal ‐norm coherence and the general ‐norm coherence, we present tradeoff relationships among the wave, particle and mixedness of quantum states. For , we establish two kinds of tradeoffs of the wave, particle and mixedness with respect to the upper and lower bounds of the ‐norm coherence given by the ‐norm coherence. These trade relations give rise to compressive understanding of the intrinsic connections among the wave, particle and mixedness of quantum states, and cover some existing results as particular ones.