Quantum state tomography via sequential uses of the same informationally incomplete measuring apparatus
Abstract
State of a d-dimensional quantum system can only be inferred by performing an informationally complete measurement with m≥slant d2 outcomes. However, an experimentally accessible measurement can be informationally incomplete. Here we show that a single informationally incomplete measuring apparatus is still able to provide all the information about the quantum system if applied several times in a row. We derive a necessary and sufficient condition for such a measuring apparatus and give illustrative examples for qubits, qutrits, general d-level systems, and composite systems of n qubits, where such a measuring apparatus exists. We show that projective measurements and L\"uders measurements with 2 outcomes are useless in the considered scenario.