  Evolution of quantum states of array of quantum dots is analyzed by means of
numerical solution of the von Neumann equation. For two qubit system with
dipole-dipole interaction and common phonon bath the evolution of the symmetric
state $\frac{\uparrow\downarrow+\downarrow\uparrow}{\sqrt{2}}$ leads to the
mixture of the triplet states, leaving the singlet decoupled. For three qubit
system ($D_{1/2}^{\otimes3}=D_{3/2}+2D_{1/2}$) with common phonon bath we
observed similar effects within the quartet state $D_{3/2}$ if all qubits were
symmetrically connected.
