Because there is some loss of information between the state before the formation of black-hole and the state after the formation of black-hole, the quantum number does not conserve under such conditions. If we initialize the state of universe as pure state and interaction term between parent universe and baby universes factorizes, the loss of quantum coherence does not exist. But it is not natural. In toy model dealing with Hawking radiation and back-reaction, it is not possible to avoid the loss of quantum coherence.