Compressive direct measurement of the quantum wave function

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

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Abstract

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
Volume113
Issue number9
DOIs
StatePublished - Aug 27 2014

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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