Abstract
An equioverlapping measurement is a rank-one POVM with the same overlap between any pair of its measurement operators. A symmetric informationally complete POVM (SIC-POVM) and an equiangular tight frame can both be equivalently formulated as special instances of an equioverlapping measurement. Due to their structural characteristics, equioverlapping measurements are interesting and useful objects in quantum foundations and practices, as partly witnessed by the extensive investigations of SIC-POVMs in quantum information theory over the last two decades and the vast literature on equiangular tight frames. In this work, we introduce and partly classify equioverlapping measurements, reveal their intrinsic properties, elucidate their similarities with, and differences from, SIC-POVMs, sets of equiangular lines, and equiangular tight frames. We show that the angles between any two measurement operators in an equioverlapping measurement can take at most three values. We further propose some open issues concerning classification, construction and optimal characterization of equioverlapping measurements.
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