Efficient quantum state tomography

Marcus Cramer (), Martin B. Plenio, Steven T. Flammia, Rolando Somma, David Gross, Stephen D. Bartlett, Olivier Landon-Cardinal, David Poulin and Yi-Kai Liu
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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

Nature Communications, 2010, vol. 1, issue 1, 1-7

Abstract: 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.

Date: 2010
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DOI: 10.1038/ncomms1147

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