Abstract
Abstract Quantum coherence serves as a defining characteristic of quantum mechanics, finding extensive applications in quantum computing and quantum communication processing. This study explores quantum block coherence in the context of projective measurements, focusing on the quantification of such coherence. Firstly, we define the correlation function between the two general projective measurements P and Q, and analyze the connection between sets of block incoherent states related to two compatible projective measurements P and Q. Secondly, we discuss the measure of quantum block coherence with respect to projective measurements. Based on a given measure of quantum block coherence, we characterize the existence of maximal block coherent states through projective measurements. This research integrates the compatibility of projective measurements with the framework of quantum block coherence, contributing to the advancement of block coherence measurement theory.
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