A. Smith, C. A. Riofrío, B. E. Anderson, H. Sosa-Martinez, I. H. Deutsch, P. S. Jessen
Recovering a full description of a complex system or process from limited information is a central problem in science and engineering. To address this, a set of techniques known as "compressed sensing" have been widely used in, for example, image compression, movie recommendation, location estimation, and earthquake analysis. In physics, one often seeks an estimate of an unknown quantum state based on a sparse set of measurements. Here we demonstrate a compressed sensing algorithm that reconstructs quantum states from continuous-time measurements performed on an ensemble of atomic spins, and compare its performance to a conventional least-squares estimator. Both approaches yield high fidelity estimates of nearly pure states from similar amounts of incomplete and noisy data, but we find compressed sensing to be significantly more robust against systematic errors. Our findings illustrate the tradeoffs inherent in quantum tomography and point the way to fast and robust state estimation in large dimensional Hilbert spaces.
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http://arxiv.org/abs/1208.5015
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