Parallelized projective measurements for spatial photonic qudits estimation

TL;DR

This paper introduces a novel quantum state tomography method for high-dimensional photonic states that requires fewer measurements by using parallelized projective measurements based on spatial multiplexing.

Contribution

The authors develop a new tomography scheme that reconstructs arbitrary d-dimensional states with only d+1 settings, demonstrated experimentally for 6-dimensional states.

Findings

Achieved high fidelity (>0.97) in state reconstruction

Reduced experimental settings from 42 to 7

Successfully reconstructed states without mutually unbiased bases

Abstract

We present a quantum state tomography method that enables the reconstruction of \emph{arbitrary} $d-$dimensional quantum states encoded in the discretized transverse momentum of photons, by using \emph{only} $d+1$ experimental settings. To this end, we identify a family of bases with the property that the outcomes of a projective measurement are \emph{spatially multiplexed} on the interference pattern of the projected state. Using the proposed scheme we performed, as a proof-of-principle, an experimental reconstruction of $d=6-$dimensional states, for which a complete set of mutually unbiased bases does not exist. We obtained fidelity values above 0.97 for both pure and mixed states, reducing the number of experimental settings from $42$ to only $7$.