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The wave-particle duality, as one of the expressions of Bohr complementarity,is usually quantified by path predictability and the visibility of interferencefringes. With the development of quantum resource theory, the quantitativeanalysis of wave-particle duality is increasing, most of which are expressed inthe form of specific functions. In this paper, we obtain the path informationmeasure for pure states by converting the coherence measure for pure state intoa symmetric concave function. Then we prove the function as a path informationmeasure is also valid for mixed states. Furthermore, we also establish ageneralized wave-particle-mixedness traility. Although the mixedness proposedin the text is not a complete mixedness measure, it also satisfies someconditions of mixdness measure. From the perspective of resource theory, thepath information we establish can be used as the measure of the resource ofpredictability, and the triaility relationship we establish reveals therelationship among coherence, predictability, purity and mixdness degree to acertain extent. According to our method, given either coherence measure or pathinformation, a particular form of wave-particle-mixedness traility can beestablished. This will play an important role in establishing connectionsbetween wave, particle and other physical quantifiers.

Generalized wave-particle-Mixdness triality for n-path interferometers