Choice of Measurement Sets in Qubit Tomography

Understand

Optimal generalized measurements for state estimation are well understood.

• However, practical quantum state tomography is typically performed using a fixed set of projective measurements and the question of how to choose these measurements has been largely unexplored in the literature.
• In this work we develop theoretical asymptotic bounds for the average fidelity of pure qubit tomography using measurement sets whose axes correspond to vertices of Platonic solids.
• We also present complete simulations of maximum likelihood tomography for mixed qubit states using the Platonic solid measurements.