Statistically efficient tomography of low rank states with incomplete measurements

摘要: The construction of physically relevant low dimensional state models, and the design appropriate measurements are key issues in tackling quantum tomography for large systems. We consider statistical problem estimating rank states set-up multiple ions tomography, investigate how estimation error behaves with a reduction number measurement settings, compared standard ion setup. present extensive simulation results showing that is robust respect to choice given rank, random selection settings can be significantly reduced only negligible increase error. an argument explain these findings based on concentration inequality Fisher information matrix. In more general setup basis we use this show certain $r$ it suffices measure $O(r\log d)$ bases achieve average over all bases. numerical evidence upto 8 atoms, supporting conjecture lower bound which, if true, would imply similar behaviour case Pauli relation problems compressed sensing also discussed.