  The finite time disentanglement or entanglement sudden death, when only one
part of the composite system is subjected to a single noise, is examined. While
it is shown that entanglement sudden death can occur when a part of the
entangled mixed state is subjected to either amplitude noise or phase noise,
local action of either of them does not cause entanglement sudden death in pure
entangled states. In contrast, depolarizing noise is shown to have an abilitiy
to cause sudden death of entanglement even in pure entangled states, when only
one part of the state is exposed to it. The result is illustrated through the
action of different noisy environments individually on a single qubit of the
so-called X class of states and an arbitrary two-qubit pure state.
