The quantum correlation between the selection of the problem and that of the solution sheds light on the mechanism of the quantum speed up

TL;DR

This paper explains quantum speed ups by demonstrating how quantum correlations allow the problem solver to have partial advanced knowledge of the solution, fundamentally changing the problem-solving mechanism.

Contribution

It introduces a quantum correlation framework linking problem and solution selection, providing a new explanation for quantum speed ups.

Findings

Quantum correlations enable partial advanced knowledge of solutions.

Quantum algorithms start with 50% of solution information known.

Both quadratic and exponential speed ups are explained by this mechanism.

Abstract

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.