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Analysing Multiparticle Quantum States

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Quantum [Un]Speakables II

Part of the book series: The Frontiers Collection ((FRONTCOLL))

Abstract

The analysis of multiparticle quantum states is a central problem in quantum information processing. This task poses several challenges for experimenters and theoreticians. We give an overview over current problems and possible solutions concerning systematic errors of quantum devices, the reconstruction of quantum states, and the analysis of correlations and complexity in multiparticle density matrices.

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Notes

  1. 1.

    This means that both, measurements and states are described by the corresponding N-fold tensor products. While such a property can be inferred for the states with the help of the de Finetti theorem [1], one should be aware that its exchangeability requirements do not apply to experiments where one actively measures first all the \(s=1\) measurements, followed by all \(s=2\) measurements and so on.

  2. 2.

    Since one typically likes to leave the choice of appropriate levels of \(\alpha \) to the reader one can also report the p-value [7] of the observed data: It is the smallest \(\alpha \) with which we would have still said “incompatible” with the test.

  3. 3.

    The new operators \(X_{r|s}\) may be necessary, since the \(M_{r|s}\) can be overcomplete or not orthogonal.

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Acknowledgments

We thank Rainer Blatt, Tobias Galla, Bastian Jungnitsch, Martin Hofmann, Lukas Knips, Thomas Monz, Sönke Niekamp, Daniel Richart, Philipp Schindler, Christian Schwemmer, and Harald Weinfurter for discussions and collaborations on the presented topics. Furthermore, we thank Mariami Gachechiladze, Felix Huber, and Nikolai Miklin for comments on the manuscript. This work has been supported by the EU (Marie Curie CIG 293993/ENFOQI, ERC Starting Grant GEDENTQOPT, ERC Consolidator Grant 683107/TempoQ), the FQXi Fund (Silicon Valley Community Foundation), and the DFG (Forschungsstipendium KL 2726/2-1).

Author information

Authors and Affiliations

  1. Faculty IV for Science and Technology, University of Siegen, 57068, Siegen, Germany

    Otfried Gühne & Tobias Moroder

  2. Department of Theoretical Physics, University of the Basque Country UPV/EHU, 48080, Bilbao, Spain

    Matthias Kleinmann

Authors
  1. Otfried Gühne
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  2. Matthias Kleinmann
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  3. Tobias Moroder
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Corresponding author

Correspondence to Otfried Gühne .

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Editors and Affiliations

  1. Faculty of Physics, University of Vienna, Vienna, Austria

    Reinhold Bertlmann

  2. Faculty of Physics, VCQ and IQOQI, University of Vienna, Vienna, Austria

    Anton Zeilinger

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Gühne, O., Kleinmann, M., Moroder, T. (2017). Analysing Multiparticle Quantum States. In: Bertlmann, R., Zeilinger, A. (eds) Quantum [Un]Speakables II. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-38987-5_21

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