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Q: Fachverband Quantenoptik und Photonik
Q 4: Quantum Information: Concepts and Methods I
Q 4.4: Talk
Monday, March 8, 2010, 14:45–15:00, E 214
Quantum state tomography via compressed sensing — •David Gross1, Yi-Kai Liu2, Steve Flammia3, Stephen Becker4, and Jens Eisert5 — 1Leibniz-Universitaet Hannover — 2California Institute of Technology — 3Perimeter Institute for Theoretical Physics — 4California Institute of Technology — 5Universitaet Potsdam
We establish novel methods for quantum state and process tomography based on compressed sensing. Our protocols require only simple Pauli measurements, and use fast classical post-processing based on convex optimization. Using these techniques, it is possible to reconstruct an unknown density matrix of rank r using O(rd logd) measurement settings, a significant improvement over standard methods that require d2 settings. The protocols are stable against noise, and extend to states which are approximately low-rank. The acquired data can be used to certify that the state is indeed close to a low-rank one, so no a priori assumptions are needed.
At the same time, new mathematical methods for analyzing the problem of low-rank matrix recovery have been obtained. The methods are both considerably simpler, and more general than previous approaches. It is shown that an unknown d× d matrix of rank r can be efficiently reconstructed given knowledge of only O(d r log2d) randomly sampled expansion coefficients with respect to any given matrix basis.