  The largest ensemble of qubits which satisfy the general transformation of
equal superposition is obtained by different methods, namely, linearity,
no-superluminal signalling and non-increase of entanglement under LOCC. We also
consider the associated quantum random walk and show that all unitary balanced
coins give the same asymmetric spatial probability distribution. It is further
illustrated that unbalanced coins, upon appropriate superposition, lead to new
unbiased walks which have no classical analogues.
