Quantitative Evaluation of Decoherence and Applications for Quantum-Dot   Charge Qubits
  We review results on evaluation of loss of information in quantum registers due to their interactions with the environment. It is demonstrated that an optimal measure of the level of quantum noise effects can be introduced via the maximal absolute eigenvalue norm of deviation of the density matrix of a quantum register from that of ideal, noiseless dynamics. For a semiconductor quantum dot charge qubits interacting with acoustic phonons, explicit expressions for this measure are derived. For a broad class of environmental modes, this measure is shown to have the property that for small levels of quantum noise it is additive and scales linearly with the size of the quantum register. 
L. Fedichkin and V. Privman