  It is known that a quantum system with finite degrees of freedom can simulate
a composite of a system and an environment if the state of the hypothetical
environment is randomized by external manipulation. We show theoretically that
any phase decoherence phenomena of a single qubit can be simulated with a
two-qubit system and demonstrate experimentally two examples: one is phase
decoherence of a single qubit in a transmission line, and the other is that in
a quantum memory. We perform NMR experiments employing a two-spin molecule and
clearly measure decoherence for both cases. We also prove experimentally that
the bang-bang control efficiently suppresses decoherence.
