Bounds on mixedness and entanglement of quantum teleportation resources

For a standard teleportation protocol, rank dependent upper bounds on Von Neumann entropy and linear entropy beyond which the states of respective ranks cease to be useful for quantum teleportation are derived analytically for a general d×d bipartite systems. For two qubit mixed states, we obtain rank dependent lower bound on concurrence below which the state is useless for quantum teleportation. For two qubit system, we construct mixed states of different ranks that exhibit theoretical rank dependent upper bounds on the measures of mixedness and lower bounds on the concurrence.