Sharing high-dimensional preparation contextuality via weak measurements with different pointers

Abstract Multiple sequential observers, each independently obtaining preparation contextual outcome statistics through measurements on an ensemble, share the preparation contextuality (PC) enabled by the ensemble. We present a circuit model for high-dimensional weak measurements to explore PC sharing in high-dimensional systems using weak measurements with different pointers. We identify the relationship between the maximum number of sequential observers, system dimension, and pointer type, and find that PC can be shared by at most two sequential observers. For two observers to successfully share PC, the required minimum measurement strength increases with the dimension. Additionally, relaxing the equal-strength constraint on the first observer’s measurements expands the strength adjustable region from a linear interval to a planar area. Finally, we present a concrete implementation of our circuit model for unsharp measurement, with applications in PC sharing and d-level parity-oblivious random access code game. Our results provide theoretical guidance for experimental realization of high-dimensional weak measurements and deepen understanding of the relationship between PC and measurement in high-dimensional systems.