Ascertaining the Values of ${\sigma }_x$, ${\sigma }_y$, and ${\sigma }_z$ 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-$\frac{1}{2}$ 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 $95.6\%$.

Figure 1

The three stages of the quantum-optical experiment that realizes the mean king’s problem.

Figure 2

Outcome of a run of the experiment in which the clicks of the gated detectors of the third stage in Fig. 1 are counted for 30 s for each of the projections (3); see text. Alice’s inferred odds for guessing Bob’s projection right exceed, in each case, the $90.2\%$ odds of the optimal single-qubit strategy, with average odds of $95.6\%\pm 1.2\%$.