title: Five Measurement Bases Determine Pure Quantum States on Any Dimension.
abstract: A long-standing problem in quantum mechanics is the minimum number of observables required for the characterization of unknown pure quantum states. The solution to this problem is especially important for the developing field of high-dimensional quantum information processing. In this work we demonstrate that any pure d-dimensional state is unambiguously reconstructed by measuring five observables, that is, via projective measurements onto the states of five orthonormal bases. Thus, in our method the total number of different measurement outcomes (5d) scales linearly with d. The state reconstruction is robust against experimental errors and requires simple postprocessing, regardless of d. We experimentally demonstrate the feasibility of our scheme through the reconstruction of eight-dimensional quantum states, encoded in the momentum of single photons.
authors.affiliation: Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile.|Center for Optics and Photonics, Universidad de Concepción, Casilla 4016, Concepción, Chile.|MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
authors.forename: D
authors.initials: D
authors.lastname: Goyeneche
authors.affiliation: Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile.|Center for Optics and Photonics, Universidad de Concepción, Casilla 4016, Concepción, Chile.|MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
authors.forename: G
authors.initials: G
authors.lastname: Cañas
authors.affiliation: Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile.|Center for Optics and Photonics, Universidad de Concepción, Casilla 4016, Concepción, Chile.|MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
authors.forename: S
authors.initials: S
authors.lastname: Etcheverry
authors.affiliation: Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile.|Center for Optics and Photonics, Universidad de Concepción, Casilla 4016, Concepción, Chile.|MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
authors.forename: E S
authors.initials: ES
authors.lastname: Gómez
authors.affiliation: Center for Optics and Photonics, Universidad de Concepción, Casilla 4016, Concepción, Chile.|MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción, Chile.|Departamento de Ingeniería Eléctrica, Universidad de Concepción, 160-C Concepción, Chile.
authors.forename: G B
authors.initials: GB
authors.lastname: Xavier
authors.affiliation: Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile.|Center for Optics and Photonics, Universidad de Concepción, Casilla 4016, Concepción, Chile.|MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
authors.forename: G
authors.initials: G
authors.lastname: Lima
authors.affiliation: Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile.|Center for Optics and Photonics, Universidad de Concepción, Casilla 4016, Concepción, Chile.|MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
authors.forename: A
authors.initials: A
authors.lastname: Delgado