Equioverlapping measurements in qutrit systems

Abstract

Overlap between quantum states or observables is a fundamental quantity in quantum theory. Equioverlapping measurements arise naturally when considering quantum measurements with equal overlap between measurement operators. This is essentially a kind of symmetric configuration for quantum measurements. The conventional von Neumann measurements and symmetric informationally complete positive operator valued measures (SIC-POVMs) are two extreme cases of equioverlapping measurements. These measurements not only have intuitive physical significance, but also have rich and subtle mathematical structures. However, they remain largely unexplored. In this work, we investigate some general features of equioverlapping measurements with focus on qutrit systems (i.e., three dimensional systems), and partially classify equioverlapping measurements in this case. We further pose the challenge of complete classification and construction of equioverlapping measurements.