To handle uncertainties and process complex in- formation from different sources, quantum mass function, an efficient method has been proposed to address this issues. On the basis of the quantum mass function, many methods has been designed to indicate the differences among quantum evidences. Nevertheless, they are developed by quantum evidence theory to process traditional basic probability assignments (QBPAs) and not applicable in measuring quaternion BPAs (QTBPAs). Therefore, in this paper, a specific customized method is proposed for the generalized form of quantum mass function, namely quaternion mass function, to accurately demonstrate the dis- tances among disparate evidences given as QTBPAs (QED). Moreover, it is a pioneer to investigate the differences between pieces of evidences in the plane space of quaternion which is reliable and strictly satisfies the axioms of distance. Besides, if QTBPAs degenerate into QBPAs, QED also degenerate into quantum evidential evidence, which indicates the consistency in this new standard of measuring distances. Consequently, QED is derived from the quantum evidential distance and possesses an extensive capability to indicate dissimilarities among QTBPAs. Several numerical examples are offered to check the validity and practical availability of QED.