Universal compressive tomography in the time-frequency domain

Quantum state tomography is a basic tool in quantum information, but it becomes a challenging task that requires an immense number of measurement configurations as the system dimension grows. We implement an adaptive compressive tomography scheme capable of reconstructing any arbitrary low-rank spectral-temporal optical signal with extremely few measurement settings and without any ad hoc assumption about the initially unknown signal. This is carried out by implementing projections onto arbitrary user-specified optical modes. We present conclusive experimental results for both temporal modes and frequency bins, which showcase the versatility of our method and thereby introduce a universal optical reconstruction framework to these platforms.