Abstract
We present a proof-of-principle demonstration of a method to characterize any pure spatial qudit of arbitrary dimension , which is based on the classic phase-shift interferometry technique. In the proposed scheme a total of only measurement outcomes are needed, implying a significant reduction with respect to the standard schemes for quantum-state tomography which require on the order of . By using this technique, we have experimentally reconstructed a large number of states ranging from up to 14 with mean fidelity values higher than 0.97. For that purpose the qudits were codified in the discretized transverse-momentum position of single photons, once they are sent through an aperture with slits. We provide an experimental implementation of the method based in a Mach-Zehnder interferometer, which allows one to reduce the number of measurement settings to four since the slits can be measured simultaneously. Furthermore, it can be adapted to consider the reconstruction of the unknown state from the outcome frequencies of fixed projectors independently of the encoding or the nature of the quantum system, allowing one to implement the reconstruction method in a general experiment.
- Received 11 July 2017
DOI:https://doi.org/10.1103/PhysRevA.96.062328
©2017 American Physical Society