Abstract

We propose an experiment that realizes a symmetric informationally complete (SIC) probability-operator measurement (POM) in the four-dimensional Hilbert space of a qubit pair. The qubit pair is carried by a single photon as a polarization qubit and a path qubit. The implementation of the SIC POM is accomplished with the means of linear optics. The experimental scheme exploits an approach to SIC POMs that uses a two-step process: a measurement with full-rank outcomes, followed by a projective measurement on a basis that is chosen in accordance with the result of the first measurement. The basis of the first measurement and the four bases of the second measurements are pairwise unbiased—a hint at a possibly profound link between SIC POMs and mutually unbiased bases.

Date

2012

Authors

Amir Kalev, Jiangwei Shang, Berthold-Georg Englert

Journal

Physical Review A—Atomic, Molecular, and Optical Physics

Volume

85

Issue

5

Pages

052115

Publisher

American Physical Society