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Goyeneche D, Cañas G, Etcheverry S, Gómez ES, Xavier GB, Lima G, Delgado A. Five Measurement Bases Determine Pure Quantum States on Any Dimension. Phys Rev Lett 2015; 115:090401. [PMID: 26371631 DOI: 10.1103/physrevlett.115.090401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2014] [Indexed: 06/05/2023]
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.
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Affiliation(s)
- D Goyeneche
- 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
| | - G Cañas
- 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
| | - S Etcheverry
- 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
| | - E S Gómez
- 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
| | - G B Xavier
- 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
| | - G Lima
- 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
| | - A Delgado
- 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
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Etcheverry S, Cañas G, Gómez ES, Nogueira WAT, Saavedra C, Xavier GB, Lima G. Quantum key distribution session with 16-dimensional photonic states. Sci Rep 2014; 3:2316. [PMID: 23897033 PMCID: PMC3727059 DOI: 10.1038/srep02316] [Citation(s) in RCA: 92] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2013] [Accepted: 07/15/2013] [Indexed: 11/25/2022] Open
Abstract
The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.
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Affiliation(s)
- S Etcheverry
- Departamento de Física, Universidad de Concepción, 160-C Concepción, Chile
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