Compressive direct measurement of the quantum wave function

Mohammad Mirhosseini, Omar S. Magaña-Loaiza, Seyed Mohammad Hashemi Rafsanjani, Robert W. Boyd

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


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.

Original languageEnglish (US)
Article number090402
JournalPhysical Review Letters
Issue number9
StatePublished - Aug 27 2014
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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