Experimental characterization of qutrits using symmetric, informationally complete positive operator-valued measures

Z. E. D. Medendorp; F. A. Torres-Ruiz; L. K. Shalm; G. N. M. Tabia; C. A. Fuchs; A. M. Steinberg

doi:10.1117/12.892130

26 July 2011 Experimental characterization of qutrits using symmetric, informationally complete positive operator-valued measures

Z. E. D. Medendorp, F. A. Torres-Ruiz, L. K. Shalm, G. N. M. Tabia, C. A. Fuchs, A. M. Steinberg

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Proceedings Volume 8001, International Conference on Applications of Optics and Photonics; 80011B (2011) https://doi.org/10.1117/12.892130
Event: International Conference on Applications of Optics and Photonics, 2011, Braga, Portugal

Abstract

Generalized quantum measurements (also known as positive operator-valued measures or POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform arbitrary POVMs in a linear-optical context. One of the most interesting POVMs, the symmetric, informationally complete-POVM (or SIC-POVM), is the most compact set of measurements that can be used to fully describe a quantum state. We use our technique to carry out the first experimental characterization of the state of a qutrit using SIC-POVMs. Because of the highly symmetric nature of this measurement, such a representation has the unique property that it permits all other measurement outcomes to be predicted by a simple extension of the classical Bayesian sum rule, making no use of complex amplitudes or Hilbert-space operators. We demonstrate this approach on several qutrit states encoded in single photons.

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Z. E. D. Medendorp, F. A. Torres-Ruiz, L. K. Shalm, G. N. M. Tabia, C. A. Fuchs, and A. M. Steinberg "Experimental characterization of qutrits using symmetric, informationally complete positive operator-valued measures", Proc. SPIE 8001, International Conference on Applications of Optics and Photonics, 80011B (26 July 2011); https://doi.org/10.1117/12.892130

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KEYWORDS

Photons

Quantum information

Projection systems

Tomography

Error analysis

Phase shifts

Mirrors

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