Measuring entangled pairs
Suppose two qubits are perfectly entangled, and therefore their measurement outcomes will be fully correlated (when they are measured in the same manner). However, the two qubits are thousands of kilometers away. By measuring one qubit, the measurement outcome of the other qubit is instantaneously known with a 100% probability. Did the information from the one measurement reach the other qubit with a speed faster then light?
This is a tough conceptual question and may great physicists have struggled to find and answer to the paradox. Einstein's theory of relativity puts an upper bound to the velocity of things: the speed of light c. Does quantum entanglement violate that rule?
The essence is here that you can never fully predict the outcome of a quantum measurement, it is a stochastic process. Once you did your measurement, you certainly know the outcome of the other qubit, but you can never fully predict the outcome of your own qubit. This insecurity of the outcome of your own measurement makes it impossible to transmit information. [1]
You could think now: why not force one of the entangled qubit in a certain state (either 1 or 0), and then measure? The other party should then measure the same outcome right? It turns out this doesn't work either. By forcing your own qubit into a certain state you break the entanglement. [2]