  Brun \emph{et al.} [Phys. Rev. Lett. \textbf{102}, 210402 (2009)] showed that
in the presence of a Deutschian closed timelike curve (D-CTC), one could
violate the Holevo bound. It is possible to utilize the Holevo bound violation
to encode $n$-bit classical information in a single qubit. Here we demonstrate
a new quantum cost efficient scheme, for storing and retrieving $n$-bit
classical information faithfully in the presence of a D-CTC in violation of the
Holevo bound. We also propose a new protocol for cloning a qubit in the
presence of a D-CTC. In both the schemes, the quantum cost is found to be of
order $O(n)$, which provides an advantage over the existing schemes having
quantum cost of exponential order.
