We present a three-qubit quantum state tomography scheme requiring a set of 17 measurement settings, significantly reducing the experimental overhead compared to the conventional 63 Pauli measurement settings. Using IBM’s 127-qubit open-access quantum processor ibm_osaka, we prepare the three-qubit W state and employ our tomography scheme to reconstruct it. Additionally, we implement a two-qubit tomography protocol, involving 7 measurement settings, on ibm_osaka to reconstruct two of the two-qubit marginals of the W state. This serves as a proof-of-principle demonstration of the well-known theoretical result that any two of the two-qubit reduced density matrices can uniquely determine most of the whole three-qubit pure states. We show that the fidelity of the W state reconstructed from its two-qubit subsystems is consistently larger than that obtained from the full three-qubit tomography, highlighting the practical advantage of the subsystem-based tomography approach.
