Figure 7: Reconstructed density matrices from full-state tomography measurements.
From: Self-healing of quantum entanglement after an obstruction
The density matrices are shown for dimensions d=2 (a–c) and d=4 (d–f). Real and imaginary parts of the reconstructed density matrices for (a) and (d) no obstruction, (b) and (e) obstruction placed 5 mm from the crystal, and (c) and (f) obstruction placed 45 mm from the crystal. It is clear that the density matrix recovers to the original unobstructed form for a two-dimensional state as well as higher-dimensional states. The density matrices were calculated by measuring an over-complete set of modes and applying a maximum-likelihood estimation using a least-squares fit to the measurements. This optimization technique ensures a density matrix with non-negative eigenvalues and a trace of unity.
