Ascertaining the Values ofσx,σy, andσzof 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-$\frac{1}{2}$ 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 $95.6\%$.