Complete state tomography of a quantum dot spin qubit

Semiconductor quantum dots are probably the preferred choice for interfacing anchored matter spin qubits and flying photonic qubits. While full tomography of a flying qubit or light polarization is, in general, straightforward, matter spin tomography is a challenging and resource-consuming task. Here we present an all-optical method for conducting full tomography of quantum dot confined spins. Our method is applicable for electronic spin configurations such as the conduction-band electron and the valence-band hole and for electron-hole pairs such as the bright and dark excitons. We excite the spin qubit using a short, resonantly tuned, polarized optical pulse, which coherently converts the qubit to an excited qubit that decays by emitting a polarized single photon. We perform the tomography by using two different orthogonal, linearly polarized excitations, followed by time-resolved measurements of the degree of circular polarization of the emitted light from the decaying excited qubit. We demonstrate our method on the dark exciton spin state with a fidelity of 0.94, mainly limited by the accuracy of our polarization analyzers.