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Phys Rev Lett. 2013 Apr 5;110(14):143601. Epub 2013 Apr 2.

Characterization of high-dimensional entangled systems via mutually unbiased measurements.

Author information

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

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.

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