We propose a measurement strategy which can, probabilistically, reproduce the statistics of any observable for spatially encoded photonic qubits. It comprises the implementation of a two-outcome positive operator-valued measure followed by a detection in a fixed transverse position, making the displacement of the detection system unnecessary, unlike previous methods. This strategy generalizes a scheme recently demonstrated by one of us and co-workers restricted to measurement of observables with equatorial eigenvectors only. The method presented here can be implemented with the current technology of programmable multipixel liquid-crystal displays. In addition, it can be straightforwardly extended to high-dimensional qudits and may be a valuable tool in optical implementations of quantum information protocols with spatial qubits and qudits.
@article{arxiv.1011.3504,
title = {Measurement strategy for spatially encoded photonic qubits},
author = {M. A. Solís-Prosser and L. Neves},
journal= {arXiv preprint arXiv:1011.3504},
year = {2010}
}