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Weak coupling with the environment damps the coherent oscillations between the states discussed in the above. The damping rate vanishes as the coupling to the environment goes to 0 .
The inverse of the damping rate is often called ‘decoherence time τ dec .
This time is essentially the quantum memory of the system, namely, after a long enough time t ＞ τ dec , the system ‘forgets’ its initial quantum state and it’s no longer coherent with the memory.
In the ideal case, it’s expected that the decoherence time τ dec → ∞ can be defined to use a quantum system as qubit.
