Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, M. J. Padgett

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We use spatial light modulators (SLMs) to measure correlations between arbitrary superpositions of orbital angular momentum (OAM) states generated by spontaneous parametric down-conversion. Our technique allows us to fully access a two-dimensional OAM subspace described by a Bloch sphere, within the higher-dimensional OAM Hilbert space. We quantify the entanglement through violations of a Bell-type inequality for pairs of modal superpositions that lie on equatorial, polar, and arbitrary great circles of the Bloch sphere. Our work shows that SLMs can be used to measure arbitrary spatial states with a fidelity sufficient for appropriate quantum information processing systems.

Original languageEnglish
Article number043844
Number of pages5
JournalPhysical Review A
Issue number4
Publication statusPublished - 30 Apr 2010


  • hidden-variable thesis
  • bell-inequality
  • quantum entanglement
  • local theories
  • light
  • photons
  • violation
  • theorem

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