Theory of unitary spin rotation and spin-state tomography for a single electron and two electrons

Electron spins in semiconductor nanostructures are considered as one of the most promising candidates of the building blocks for quantum information processing. Initialization, coherent manipulation, and measurement of a single electron spin have been recently established. Here we explore the possibility to manipulate and measure by optical means the states of two electrons as a single qubit in nanostructures and propose methods of spin-state tomography based on Faraday or Kerr rotation for cases of both a single electron and two electrons, as well as a method of the Bell-state measurement for two electrons.