Compressive direct measurement of the quantum wave function.

  title={Compressive direct measurement of the quantum wave function.},
  author={Mohammad Mirhosseini and Omar S. Maga{\~n}a-Loaiza and Seyed Mohammad Hashemi Rafsanjani and Robert W. Boyd},
  journal={Physical review letters},
  volume={113 9},
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… 

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