State Tomography of Qubit Systems Using Linear Regression Estimation and Adaptive Measurements **This work was supported by the Australian Research Council’s Discovery Projects funding scheme under Project DP130101658 and the National Natural Science Foundation of China under Grants (Nos. 61222504, 11574291, 61374092, 61621003 and 61227902).

Quantum state tomography is one of the critical tasks in the development of quantum technology. This paper further investigates the adaptive linear regression estimation (ALRE) method that was developed recently for state reconstruction of qubit systems. In this method, adaptive measurements are used to improve the performance of state reconstruction where current measurement basis is adaptively optimized based on previous knowledge through minimizing an index related to the mean squared error (MSE). The numerical results on single-qubit and two-qubit systems demonstrate the effectiveness of this proposed adaptive estimation method over static one for quantum state reconstruction.