The task to estimate all the parameters of an unknown quantum state, also called quantum state tomography, is essential for characterizing and controlling quantum systems. In this paper, we utilize observable time tra...The task to estimate all the parameters of an unknown quantum state, also called quantum state tomography, is essential for characterizing and controlling quantum systems. In this paper, we utilize observable time traces to identify the initial quantum state of a closed quantum system, based on the state space approach in the control theory. In the informationally complete scenario, we show that with a linear regression estimation (LRE), the mean squared error (MSE) scales as , where N is the resource number. In the informationally incomplete scenario, we introduce regularization LRE to perform the state tomography task. We employ PBH test to demonstrate that closed quantum systems with only one observable are informationally incomplete and propose using observables, where d is the dimension of the quantum state, for informational completeness. Numerical examples demonstrate the effectiveness of our method.展开更多
基金supported by the National Natural Science Foundation of China(Nos.62173229,12288201)the Australian Research Council Future Fellowship Funding Scheme under Project FT220100656 and the Discovery Project Funding Scheme under Project DP210101938.
文摘The task to estimate all the parameters of an unknown quantum state, also called quantum state tomography, is essential for characterizing and controlling quantum systems. In this paper, we utilize observable time traces to identify the initial quantum state of a closed quantum system, based on the state space approach in the control theory. In the informationally complete scenario, we show that with a linear regression estimation (LRE), the mean squared error (MSE) scales as , where N is the resource number. In the informationally incomplete scenario, we introduce regularization LRE to perform the state tomography task. We employ PBH test to demonstrate that closed quantum systems with only one observable are informationally incomplete and propose using observables, where d is the dimension of the quantum state, for informational completeness. Numerical examples demonstrate the effectiveness of our method.
