The direct measurement of a complex wave function has been recently realized by using weak values. In this Letter, we introduce a method that exploits sparsity for the compressive measurement of the transverse spatial wave function of photons. The procedure involves weak measurements of random projection operators in the spatial domain followed by postselection in the momentum basis. Using this method, we experimentally measure a 192-dimensional state with a fidelity of 90% using only 25 percent of the total required measurements. Furthermore, we demonstrate the measurement of a 19200-dimensional state, a task that would require an unfeasibly large acquiring time with the standard direct measurement technique. © 2014 American Physical Society.
Publication Source (Journal or Book title)
Physical Review Letters
Mirhosseini, M., Magaña-Loaiza, O., Hashemi Rafsanjani, S., & Boyd, R. (2014). Compressive direct measurement of the quantum wave function. Physical Review Letters, 113 (9) https://doi.org/10.1103/PhysRevLett.113.090402