Fast entanglement detection for unknown states of two spatial qutrits

TL;DR

This paper evaluates a practical, low-cost method for detecting entanglement in unknown two-qutrit states encoded in single photons, using partial measurements and semi-definite programming to generate optimal entanglement witnesses.

Contribution

It demonstrates the effectiveness of a semi-definite programming approach for rapid entanglement detection with reduced measurement requirements compared to full tomography.

Findings

Method detects entanglement with lower measurement cost.

Numerical results confirm effectiveness for unknown states.

Approach is practical for quantum information applications.

Abstract

We investigate the practicality of the method proposed by Maciel et al. [Phys. Rev. A. 80, 032325(2009)] for detecting the entanglement of two spatial qutrits (3-dimensional quantum systems), which are encoded in the discrete transverse momentum of single photons transmitted through a multi-slit aperture. The method is based on the acquisition of partial information of the quantum state through projective measurements, and a data processing analysis done with semi-definite programs. This analysis relies on generating gradually an optimal entanglement witness operator, and numerical investigations have shown that it allows for the entanglement detection of unknown states with a cost much lower than full state tomography.