Teleportation with an imperfect state

The standard teleportation protocol requires the availability of a maximally entangled state. Because such states are difficult to consistently generate experimentally, we study teleportation in which the entanglement used need not be maximal. The relationship between the pure state sent and the mixed state received is shown to define a convex linear, trace preserving, completely positive map on the set of 2×2 density operators–in the formal sense of quantum information theory, a qubit channel–and in fact, one whose Bloch representation is diagonal. We then calculate the amount of classical information that can be teleported using a given amount of entanglement. This analysis leads to a remarkable discovery: that the standard measure of entanglement for bipartite states is not correlated with the amount of information that can be teleported using an entangled state.