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Quantum Tomography

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Exploring Quantum Foundations with Single Photons

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

In practice, the experimenter always has to verify that the three components of a quantum experiment—state preparation, transformation, and measurement—are close to what the theorist wants them to be.

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Notes

  1. 1.

    As discussed in Ref. [9], maximum likelihood estimation is a frequentist tool, which works in the asymptotic limit of infinite sample size, but “applying a frequentist method to relatively small amounts of data is inherently disaster-prone”.

  2. 2.

    This is sufficient to describe a large range of joint system-environment dynamics including common error channels, and to illustrate the technique [40, 43], although a slightly larger environment would be required in the most general case [44, 45].

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Acknowledgements

The second part of this chapter is based on work that was first published in Ref. [18], and I have incorporated large part of the text of that paper. I would particularly like to acknowledge Christopher Wood, who was chiefly responsible for the theory developed for both, reconstruction and analysis, used in that paper, which also forms part of his PhD thesis submitted to the University of Waterloo. I have included much of this work here, as it is a vital component for the experimental application of the introduced technique. Furthermore, I would like to gratefully acknowledge Christopher Wood for introducing me to the tensor network notation and the quantum tomography methodology that I am using throughout this chapter.

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  1. School of Mathematics and Physics, The University of Queensland, Queensland, QLD, Australia

    Martin Ringbauer

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Ringbauer, M. (2017). Quantum Tomography. In: Exploring Quantum Foundations with Single Photons. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-64988-7_2

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