  This thesis deals with the generation, estimation and preservation of novel
quantum states of two and three qubits, on an NMR quantum information
processor. Using the maximum likelihood ansatz, we have developed a method for
state estimation such that the reconstructed density matrix does not have
negative eigenvalues and the errors are within the space of valid density
operators. Due to interactions with the environment, unwanted changes occur in
the system, leading to decoherence. Controlling decoherence is one of the
biggest challenges to be overcome to build quantum computers. We have used
several experimental strategies to decouple the quantum system from its
environment. These strategies are based on how much we know about
system-environment interaction and what states we want to preserve. We first
consider a case where we are aware of the system state but have no knowledge
about its interaction with the environment. We demonstrate the efficacy of the
super-Zeno scheme to tackle decoherence in this case. Then we consider a
situation where only the subspace is known to which the system state belongs.
To address such a situation we used a nested Uhrig dynamical decoupling scheme.
Next, we consider situations where we have knowledge of the state of the system
as well as its interaction with the environment. In such situations, since the
noise model is known, decoupling strategies can be explicitly designed to
cancel this noise. Using these decoupling strategies, we can experimentally
extend the lifetime of time-invariant discord of two-qubit Bell-diagonal states
and are also able to preserve the entanglement of three NMR qubits, to a
remarkable extent.
