Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry

PEARS STEFANO, QUIMEY; REBÓN, LORENA; LEDESMA, SILVIA; IEMMI, CLAUDIO

Physical Review A

AMER PHYSICAL SOC

Lugar: New York; Año: 2017 vol. 96

2469-9926

We present a proof-of-principle demonstration of a method to characterize any pure spatial qudit of arbitrarydimension d, which is based on the classic phase-shift interferometry technique. In the proposed scheme a total ofonly 4d measurement outcomes are needed, implying a significant reduction with respect to the standard schemesfor quantum-state tomography which require on the order of d2. By using this technique, we have experimentallyreconstructed a large number of states ranging from d = 2 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 d slits. We provide an experimental implementation of the methodbased in a Mach-Zehnder interferometer, which allows one to reduce the number of measurement settings to foursince the d slits can be measured simultaneously. Furthermore, it can be adapted to consider the reconstructionof the unknown state from the outcome frequencies of 4d − 3 fixed projectors independently of the encoding orthe nature of the quantum system, allowing one to implement the reconstruction method in a general experiment.