Figure 1

(Color online) The cube corresponds to all positive unital trace-preserving maps. The condition of complete positivity confines quantum channels into the tetrahedron with (generalized) Pauli matrices as vertices. In this picture the set of decoherence channels ${\mathcal{D}}_{\mathcal{B}}$ forms a line connecting the points $I$ and $S_z$.Reuse & Permissions

Figure 2

(Color online) The decoherence of a qubit governed by Eq. (5.6). The Bloch sphere that represents the initial state space of a qubit is mapped into the line connecting the decoherence basis states. On the right the evolution of Bloch-vector components for two different initial states is depicted.Reuse & Permissions

Figure 3

(Color online) The behavior of entanglement as a function of number $n$ of collisions between the system qubit and reservoir qubits. The degree of entanglement between the system qubit and $n$ reservoir qubits after $n$ collisions is given by ${\tau }_0$—it increases with the number of collisions (time) to a steady-state value. On the contrary, all reservoir qubits after their interaction with the system qubit are entangled with the constant degree of entanglement (see the tangle ${\tau }_k$). The bipartite entanglement ${\tau }_{0k}$ (the square of the concurrence $C_{0k}$) is zero until the $k\mathrm{th}$ reservoir qubit collides with the system qubit. After the collision the entanglement takes a nonzero value, though it decreases due to subsequent collisions of the system qubit with other reservoir qubits. It is interesting to note that all ${\tau }_{0k}\left(n\right)$ for $n⩾k$ are described by the same function. We assume the following initial state of the system qubit: $\mid \psi ⟩=(1∕\sqrt{2})(\mid 0⟩+\mid 1⟩)$ and ${\mid ⟨{\psi }_0\mid {\psi }_1⟩\mid }^2=0.75$.Reuse & Permissions