Analyzing quantum simulators efficiently: Scalable state tomography and quantifying entanglement with routine measurements

Conventional full state tomography reaches its limit already for a few qubits and hence novel methods for the verification and benchmarking of quantum devices are called for. We show how the complete reconstruction of density matrices is possible even if one relies only on local information about the state. This results in an experimental effort that is linear in the number of qubits and efficient post-processing -- in stark contrast to the exponential scaling of standard tomography. Whenever full tomography is not needed but instead less information required, one would expect that even fewer measurements suffice. Taking entanglement content of solid state samples and bosons in lattices as an example, we show how it may be quantified unconditionally using already routinely performed measurements only.\\ {\em Scalable reconstruction of density matrices}, T. Baumgratz, D. Gross, M. Cramer, and M.B. Plenio, arXiv:1207.0358.\\ {\em Efficient quantum state tomography}, M. Cramer, M.B. Plenio, S.T. Flammia, R. Somma, D. Gross, S.D. Bartlett, O. Landon-Cardinal, D. Poulin, and Y.-K. Liu, Nat. Commun. 1, 149 (2010).\\ {\em Measuring entanglement in condensed matter systems}, M. Cramer, M.B. Plenio, and H. Wunderlich, Phys. Rev. Lett. 106, 020401 (2011).