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

• URL: http://arxiv.org/abs/2306.07248v4
• Date: Wed, 29 May 2024 17:00:11 GMT
• Title: Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
• Authors: Gábor Drótos, Károly F. Pál, Tamás Vértesi,
• Abstract summary: Self-testing is a powerful method for certifying quantum systems. In this study, we focus on the self-testing of a specific type of non-projective qubit measurements. Our results pave the way towards self-testing any extremal qubit POVM within a potentially minimal PM scenario.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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