TY - JOUR T1 - Efficient quantum state tomography JF - Nature Communications Y1 - 2010 A1 - Marcus Cramer A1 - Martin B. Plenio A1 - Steven T. Flammia A1 - David Gross A1 - Stephen D. Bartlett A1 - Rolando Somma A1 - Olivier Landon-Cardinal A1 - Yi-Kai Liu A1 - David Poulin AB - Quantum state tomography, the ability to deduce the state of a quantum system 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 infeasible because the number of quantum measurements and the amount of computation required to process them grows exponentially in the system size. Here we show that we can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. We present two schemes for tomography in 1-D quantum systems and touch on generalizations. One scheme requires unitary operations on a constant number of subsystems, while the other requires only local measurements together with more elaborate post-processing. Both schemes rely only on a linear number of experimental operations and classical postprocessing that is polynomial in the system size. A further strength of the methods is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions. VL - 1 U4 - 149 UR - http://arxiv.org/abs/1101.4366v1 CP - 9 J1 - Nat Comms U5 - 10.1038/ncomms1147 ER -