• Open Access

Characterization of High-Dimensional Entangled Systems via Mutually Unbiased Measurements

D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. J. Padgett
Phys. Rev. Lett. 110, 143601 – Published 2 April 2013
PDFHTMLExport Citation

Abstract

Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases can be hard to implement. We show experimentally that efficient quantum state reconstruction of a high-dimensional multipartite quantum system can be performed by considering only the MUBs of the individual parts. The state spaces of the individual subsystems are always smaller than the state space of the composite system. Thus, the benefit of this method is that MUBs need to be defined for the small Hilbert spaces of the subsystems rather than for the large space of the overall system. This becomes especially relevant where the definition or measurement of MUBs for the overall system is challenging. We illustrate this approach by implementing measurements for a high-dimensional system consisting of two photons entangled in the orbital angular momentum degree of freedom, and we reconstruct the state of this system for dimensions of the individual photons from d=2 to 5.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 20 December 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.143601

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

D. Giovannini1,*, J. Romero1,2, J. Leach3, A. Dudley4, A. Forbes4,5, and M. J. Padgett1

  • 1School of Physics and Astronomy, SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
  • 2Department of Physics, SUPA, University of Strathclyde, Glasgow G4 ONG, United Kingdom
  • 3School of Engineering and Physical Sciences, SUPA, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
  • 4CSIR National Laser Centre, PO Box 395, Pretoria 0001, South Africa
  • 5School of Physics, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa

  • *d.giovannini.1@research.gla.ac.uk

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand
Issue

Vol. 110, Iss. 14 — 5 April 2013

Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×