Variational quantum tomography with incomplete information by means of semidefinite programs
Abstract
We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite Programs. Numerical simulations indicate that the estimated state does not overestimate purity, and neither the expectation value of optimal entanglement witnesses. The convergence properties of the method are similar to compressed sensing approaches, in the sense that, in order to reconstruct low rank states, it needs just a fraction of the effort correspondig to an informationally complete measurement.
Cite
@article{arxiv.1001.1793,
title = {Variational quantum tomography with incomplete information by means of semidefinite programs},
author = {Thiago O. Maciel and André T. Cesário and Reinaldo O. Vianna},
journal= {arXiv preprint arXiv:1001.1793},
year = {2011}
}
Comments
8 pages, 6 figures. In the previous version there was a mistake about lower bounds to arbitrary expectation values. It is now corrected