Stuttgart 2012 – wissenschaftliches Programm
Q 8.3: Vortrag
Montag, 12. März 2012, 14:30–14:45, V38.04
Statistical tests for quantum state reconstruction I: Theory — •Matthias Kleinmann1, Tobias Moroder1,2, Thomas Monz3, Philipp Schindler3, Otfried Gühne1, and Rainer Blatt2,3 — 1Naturwissenschaftlich-Technische Fakultät, Universität Siegen — 2Institut für Quantenoptik und Quanteninformation, Innsbruck — 3Institut für Experimentalphysik, Universität Innsbruck
In quantum state tomography and similar schemes, the measured data is usually not used directly but rather becomes subject of a sophisticated reconstruction procedure that squeezes the data into a quantum state. In general such techniques are only admissible if the statistical error - as due to low sampling - dominates over the systematical errors, such as misaligned measurement bases. We here present tests that allow to detect situations in which a state reconstruction will become statistically inadmissible. In particular, the positivity of the density operator and the linear dependencies that occur in overcomplete tomography lead to strong conditions on the measured data. Furthermore, we argue, that certain unphysical properties of naive reconstruction schemes are merely statistical effects and hence can be safely ignored in many situations.