Self-testing criteria for preparing-measuring qubit system

Abstract

Self-testing is a high level of security verification of a claimed quantum device, confirming the quantum states prepared in the device and the measurements performed based solely on the observed statistics. The statistical correlations can realize the self-testing of the quantum system in the prepare-and-measurement scenario. However, most of the previous studies focused on the self-testing of shared entangled states between devices, only a few works have been presented and the existing works can only simultaneously self-test the states and measurements when some witness inequalities reach the maximum violation. We focus on four states preparation and two measurements chosen scenario. In this scenario, Armin Tavakoli et al have put forward a criterion based on the dimensional witness violation inequality which can achieve BB84 particles and corresponding Pauli measurements. However, in addition to the maximum violation of the inequality, any statistics with deviation from the maximum deviation can not be self-tested. Besides, only the BB84 particle preparation and measurements system can be self-tested with that criterion, resulting in a large number of four states' preparation and two measurement systems that can not be self-tested. Therefore, in this paper, in addition to the maximum violation of that dimension inequality, we directly focus on the full observed statistics and further propose some new criteria for self-testing qubit quantum systems in the prepare-and-measurements scenario. And give proof of the self-testing criteria in the ideal case. We construct a local isometry with the constructions commonly used in device-independent cases, exchange the target system with the additional system, and realize the self-testing of more qubit state sets and measurement sets than BB84 particles. This meets the requirements of practical experiments to realize various tasks by different quantum state sets. In addition, we perform a robust analysis of the proposed criteria and use fidelity to describe the closeness of the state to the ideal state of the auxiliary system. Finally, an improved dimensional-dependent NPA method was used to optimize the lower bound of the robustness, making the new criteria practical under experimental noise. We use the YALIMP software package in MATLAB and the solver SEDUMI to achieve this optimization problem. The research increases the diversity of qubit state preparations and measurement system self-testing, which is beneficial to the actual self-testing of different non-entangled single quantum systems.

Dynamic change characteristics of wetlands in Hefei and their driving factors along the urban–rural gradient

“…In contrast to other methods, GeoDetector can overcome the limitations of conventional statistical analysis methods and does not need linear assumptions. GeoDetector proves to be an effective instrument for discerning the roles of individual factors and their interactions (Wang and Xu 2017). This approach better aligns with the paper's requirements for the quantitative evaluation of the contributions of individual indicators, encompassing both the ecological surroundings and anthropogenic interventions, as well as their interactions.…”

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