Mainz 2017 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 23: Quantum Information: Concepts and Methods IV

Q 23.6: Vortrag

Dienstag, 7. März 2017, 15:45–16:00, P 2

Multiqubit State Tomography from a Physical Perspective — •Lukas Knips1,2, Christian Schwemmer1,2, Nico Klein1,2, Jonas Reuter3, Géza Tóth4,5,6, and Harald Weinfurter1,21Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching — 2Department für Physik, Ludwig-Maximilians-Universität, D-80797 München — 3Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn — 4Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spanien — 5IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spanien — 6Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Ungarn

We show how the statistical nature of measurements alone easily causes unphysical estimates in quantum state tomography. Multinomial or Poissonian noise results in eigenvalue distributions converging to the Wigner semicircle distribution for already a modest number of qubits. This fact enables to estimate the influence of finite statistics to state tomography as well as the number of measurements necessary to avoid unphysical solutions. More importantly knowing the impact of statistical noise on the eigenvalue distribution directly leads to a physical state estimate with minimal numerical effort. Combining ideas from random matrix theory with pertubation theory, one can immediately obtain a physically motivated estimate together with confidence regions for the state estimate as well as for interesting figures of merit like the fidelity.

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