Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario

Abstract

Self-testing is a powerful method for certifying quantum systems. Initially proposed in the device-independent (DI) setting, self-testing has since been relaxed to the semi-device-independent (semi-DI) setting. In this study, we focus on the self-testing of a specific type of non-projective qubit measurements belonging to a one-parameter family, using the semi-DI prepare-and-measure (PM) scenario. Remarkably, we identify the simplest PM scenario discovered so far, involving only four preparations and four measurements, for self-testing the fourth measurement. This particular measurement is a four-outcome non-projective positive operator-valued measure (POVM) and falls in the class of semisymmetric informationally complete (semi-SIC) POVMs introduced by Geng et al. [Phys. Rev. Lett. 126, 100401 (2021)]. To achieve this, we develop analytical techniques for semi-DI self-testing in the PM scenario. Our results shall pave the way towards self-testing any extremal qubit POVM within a potentially minimal PM scenario.

28 pages, 2 figures. Please note that this is currently a pre-publication version that differs from published article in a few places

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• Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios
• Experimental certification of ensembles of high-dimensional quantum states with independent quantum devices
• Translating Bell Non-Locality to Prepare-and-Measure Scenarios under Dimensional Constraints
• Certifying asymmetry in the configuration of three qubits
• Communication scenario enables robust self-testing of n-party Greenberger-Horne-Zeilinger basis measurements