Universal compressive tomography in the time-frequency domain

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