title: Compressive direct measurement of the quantum wave function.
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.
authors.affiliation: The Institute of Optics, University of Rochester, Rochester, New York 14627, USA.
authors.forename: Mohammad
authors.initials: M
authors.lastname: Mirhosseini
authors.affiliation: The Institute of Optics, University of Rochester, Rochester, New York 14627, USA.
authors.forename: Omar S
authors.initials: OS
authors.lastname: Magaña-Loaiza
authors.affiliation: Center for Coherence and Quantum Optics and the Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.
authors.forename: Seyed Mohammad
authors.initials: SM
authors.lastname: Hashemi Rafsanjani
authors.affiliation: The Institute of Optics, University of Rochester, Rochester, New York 14627, USA and Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada.
authors.forename: Robert W
authors.initials: RW
authors.lastname: Boyd