Efficient quantum state tomography
Abstract
Quantum state tomographydeducing quantum states from measured datais 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 postprocessing. Both rely only on a linear number of experimental operations and postprocessing 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.
 Publication:

Nature Communications
 Pub Date:
 December 2010
 DOI:
 10.1038/ncomms1147
 arXiv:
 arXiv:1101.4366
 Bibcode:
 2010NatCo...1..149C
 Keywords:

 Quantum Physics
 EPrint:
 9 pages, 4 figures. Combines many of the results in arXiv:1002.3780, arXiv:1002.3839, and arXiv:1002.4632 into one unified exposition