Orthogonalised Self-Guided Quantum Tomography: Insights from Single-Pixel Imaging

We introduce the concept of self-guided imaging (SGI) as a linear analogue of self-guided quantum tomography (SGQT). We show that SGI is mathematically equivalent to single-pixel imaging (SPI). Taking inspiration from orthogonalised ghost imaging, a recent advance in SPI, we introduce orthogonalised SGQT. This requires no additional experimental overhead and leads to faster and more accurate final convergence, as we demonstrate numerically (fidelity $95.2\% \rightarrow 99.17\%$) and experimentally (fidelity $92.1\% \rightarrow 95.3\%$). This work suggests that further routines from SPI and SGQT can be interchanged to optimise measurements and convergence.