Spin-Polarized Initialization and Readout for Single-Qubit State Tomography
We propose a theoretical protocol for reconstructing the density matrix of a single-electron spin qubit using spin-polarized transport. The system consists of a quantum dot coupled to ferromagnetic reservoirs and subject to a magnetic field lying in the $xy$ plane of the Bloch sphere. Spin-dependent tunneling events measured along the $x\pm$, $y\pm$, and $z\pm$ quantization axes give rise to probability distributions that encode the quantum state of the qubit. The open-system dynamics are described using a Lindblad master equation, which captures the time evolution of the spin under continuous coupling to the reservoirs. By counting tunneling events for four different magnetic alignments, we formulate a scheme for reconstructing the full density matrix of the qubit. The resulting simulation data are analyzed using machine-learning techniques to process the measured probability distributions and infer the corresponding density matrix elements. The proposed model enables complete access to the open-system density matrix, including both population probabilities and relative phase information. Successful state reconstruction demonstrates the validity and robustness of the approach, highlighting its applicability to experimentally accessible spin-transport platforms.