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Efficient quantum state tomography

Author

Listed:
  • Marcus Cramer

    (Institut für Theoretische Physik, Universität Ulm)

  • Martin B. Plenio

    (Institut für Theoretische Physik, Universität Ulm)

  • Steven T. Flammia

    (Perimeter Institute for Theoretical Physics)

  • Rolando Somma

    (Perimeter Institute for Theoretical Physics)

  • David Gross

    (Institute for Theoretical Physics, Leibniz University Hannover)

  • Stephen D. Bartlett

    (School of Physics, The University of Sydney, Sydney)

  • Olivier Landon-Cardinal

    (Université de Sherbrooke)

  • David Poulin

    (Université de Sherbrooke)

  • Yi-Kai Liu

    (University of California)

Abstract

Quantum state tomography—deducing quantum states from measured data—is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes unfeasible because the number of measurements and the amount of computation required to process them grows exponentially in the system size. Here, we present two tomography schemes that scale much more favourably than direct tomography with system size. One of them requires unitary operations on a constant number of subsystems, whereas the other requires only local measurements together with more elaborate post-processing. Both rely only on a linear number of experimental operations and post-processing that is polynomial in the system size. These schemes can be applied to a wide range of quantum states, in particular those that are well approximated by matrix product states. The accuracy of the reconstructed states can be rigorously certified without any a priori assumptions.

Suggested Citation

  • Marcus Cramer & Martin B. Plenio & Steven T. Flammia & Rolando Somma & David Gross & Stephen D. Bartlett & Olivier Landon-Cardinal & David Poulin & Yi-Kai Liu, 2010. "Efficient quantum state tomography," Nature Communications, Nature, vol. 1(1), pages 1-7, December.
    • Handle: RePEc:nat:natcom:v:1:y:2010:i:1:d:10.1038_ncomms1147
    DOI: 10.1038/ncomms1147
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    Cited by:

    1. Bao, Daipengwei & Liu, Min & Ou, Yangwei & Xu, Qingshan & Li, Qin & Tan, Xiaoqing, 2024. "Eigenvalue-based quantum state verification of three-qubit W class states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).

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