Sizing up entanglement in mutually unbiased bases with Fisher information

An efficient method for assessing the quality of quantum state tomography is developed. Special attention is paid to the tomography of multipartite systems in terms of unbiased measurements. Although the overall reconstruction errors of different sets of mutually unbiased bases are the same, differences appear when particular aspects of the measured system are contemplated. This point is illustrated by estimating the fidelities of genuinely tripartite entangled states.