Quantum correlation between the selection of the problem and that of the solution sheds light on the mechanism of the quantum speed-up
Giuseppe Castagnoli · Physical Review A · 2010
In classical problem solving, there is, of course, correlation between the selection of the problem on the part of Bob (the problem setter) and that of the solution on the part of Alice (the problem solver). In quantum problem solving, this correlation becomes quantum. This means that Alice contributes to selecting $50%$ of the information that specifies the problem. As the solution is a function of the problem, this gives to Alice advanced knowledge of $50%$ of the information that specifies the solution. Both the quadratic and exponential speed-ups are explained by the fact that quantum algorithms start from this advanced knowledge.