Ascertaining the Values of $σ_x$, $σ_y$, and $σ_z$ of a Polarization Qubit

In the 1987 spin retrodiction puzzle of Vaidman, Aharonov, and Albert one is challenged to ascertain the values of $\sigma_x$, $\sigma_y$, and $\sigma_z$ of a spin-1/2 particle by utilizing entanglement. We report the experimental realization of a quantum-optical version in which the outcome of an intermediate polarization projection is inferred by exploiting single-photon two-qubit quantum gates. The experimental success probability is consistently above the 90.2% threshold of the optimal one-qubit strategy, with an average success probability of 95.6%.