  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 a
novel 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, the valence-band hole, and for electron-hole pairs
such as the bright and the dark exciton. We excite the spin qubit using 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 fidelity of 0.94,
mainly limited by the accuracy of our polarization analyzers.
