Use of maximally entangled states in dense coding and quantum teleportation

Question

In studying about the procedures of superdense coding and quantum teleportation, I have seen that maximally entangled states are used in both cases to show that how entanglement can be used as resource. Why are arbitrary entangled states (not necessarily maximally entangled) not used? What is the speciality of maximally entangled states that they are specifically used in the discussions?

Answer 1

Maximally entangled states just work better for these two applications:

• for superdense coding, you need an orthonormal basis which can be mapped between each other using unitaries that are local to just one qubit. If you used $\alpha|00\rangle+\beta|11\rangle$ (you don't lose generality here, due to the Schmidt decomposition), then applying $X$ to one qubit produces an orthogonal state, but unless $|\alpha|=1/\sqrt{2}$, there is no other unitary that produces a different orthogonal state. That means your procedure one transmits 1 bit, not 2.

• for teleportation, the important thing is to be able to correct for getting all the possible different measurement results. For any entangled state, you could probably make a scheme that would work for specific measurement outcomes (at worst, I can probabilistically convert the state into a maximally entangled state). But it has to work for all outcomes. Again, the key is essentially that the Bell basis consists of 4 orthonormal states that can be mapped to each other by local Pauli rotations. We can propagate the Paulis through the circuit and see how to correct them. If the state isn't maximally entangled, we don't have that property.