Compressive Direct Measurement of the Quantum Wave Function

Mohammad Mirhosseini, Omar S. Magaña-Loaiza, Seyed Mohammad Hashemi Rafsanjani, and Robert W. Boyd
Phys. Rev. Lett. 113, 090402 – Published 27 August 2014

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 19 200-dimensional state, a task that would require an unfeasibly large acquiring time with the standard direct measurement technique.

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  • Received 13 May 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.090402

© 2014 American Physical Society

Authors & Affiliations

Mohammad Mirhosseini1,*, Omar S. Magaña-Loaiza1, Seyed Mohammad Hashemi Rafsanjani2, and Robert W. Boyd1,3

  • 1The Institute of Optics, University of Rochester, Rochester, New York 14627, USA
  • 2Center for Coherence and Quantum Optics and the Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
  • 3Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

  • *mirhosse@optics.rochester.edu

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Vol. 113, Iss. 9 — 29 August 2014

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