[attilakun]

But you _can_ decide what to send! It's just that the sending is never faster than the speed of light because it always involves the transportation of some physical stuff. In the case of superdense coding, you have to send one half of an entangled particle-pair which can't be done faster than the speed of light. The benefit is that you can send 2 bits of classical information by transporting only one (entangled) qubit.

In case of quantum teleportation, you need to send two bits of classical information via whatever mechanism you want to use which again can't be done faster than the speed of light. The benefit is that you can transport the quantum-state of the sender's qubit.

[evanb]

In superdense coding you send one quantum bit ahead of time and hang onto it’s entangled partner. Then later you send one classical but which, when combined with the quantum bit you shared earlier, conveys two classical bits of your choice.

[attilakun]

You don't send any classical bits in superdense coding. You start out with a pair of entangled qubits in the state |00>+|11>. Then, if Alice has the first qubit and Bob has the second, by manipulating the first qubit Alice can perform 4 actions:

1. Nothing, which leaves the combined state unchanged: |00>+|11>.

2. Flip the sign of the base state |11>, thereby changing the combined state to |00>-|11>.

3. Flip the first bit which changes the combined state to |10>+|01>.

4. Perform choice 3 and flip the sign of base state |10>, which changes the combined state to -|10>+|01>.

Now notice that all 4 possible combined states are orthogonal to each other. But we reached each orthogonal state by manipulating only Alice's qubit. When Bob receives Alice's qubit he can put the 2 qubits together and see which state the combined system is in. You wouldn't be able to do this by sending a classical bit as that can't participate in entanglement. And entanglement is needed to access 4 different orthogonal states via manipulating just one qubit.

[evanb]

You're right---I forgot the protocol. Thanks for the correction!