A. B. Klimov

We study the physical implementation of an optimal tomographic reconstruction scheme for the case of determining the state of a multi-qubit system, where trapped ions are used for defining qubits. The protocol is based on the use of mutually unbiased measurements and on the physical information described in H. Häffner \emph{et. al} [Nature \textbf{438}, 643-646 (2005)]. We introduce the concept of physical complexity for different types of unbiased measurements and analyze their generation in terms of one and two qubit gates for trapped ions.

We present a method of treating the interaction of a single three-level ion with two laser beams. The idea is to apply a unitary transformation such that the exact transformed Hamiltonian has one of the three levels decoupled for all values of the detunings. When one takes into account damping, the evolution of the system is governed by a master equation usually obtained via adiabatic approximation under the assumption of far-detuned lasers. To go around the drawbacks of this technique, we use the same unitary transformation to get an effective master equation.