We study the efficiency of two-qubit mixed entangled states as resources for quantum teleportation. We first consider two maximally entangled mixed states, viz., the Werner state\cite{werner}, and a class of states introduced by Munro {\it et al.} \cite{munro}. We show that the Werner state when used as teleportation channel, gives rise to better average teleportation fidelity compared to the latter class of states for any finite value of mixedness. We then introduce a non-maximally entangled mixed state obtained as a convex combination of a two-qubit entangled mixed state and a two-qubit separable mixed state. It is shown that such a teleportation channel can outperform another non-maximally entangled channel, viz., the Werner derivative for a certain range of mixedness. Further, there exists a range of parameter values where the former state satisfies a Bell-CHSH type inequality and still performs better as a teleportation channel compared to the Werner derivative even though the latter violates the inequality.
Three-qubit mixed states are used as a channel for controlled quantum teleportation (CQT) of single-qubit states. The connection between different channel parameters to achieve maximum controlled teleportation fidelity is investigated. We show that for a given multipartite entanglement and mixedness a class of non-maximally-entangled mixed
X states (
X-NMEMS) achieves optimum controlled quantum teleportation fidelity; interestingly a class of maximally entangled mixed
X states (
X-MEMS) fails to do so. This demonstrates, for a given spectrum and mixedness, that
X-MEMS are not sufficient to attain optimum controlled quantum teleportation fidelity, which is in contradiction with the traditional quantum teleportation of single qubits. In addition, we show that biseparable
X-NMEMS, for a certain range of mixedness, are useful as a resource to attain high controlled quantum teleportation fidelity, which essentially lowers the requirements of quantum channels for CQT.