The "No Free Lunch Theorem" says: that when averaged across all possible problems, any two strategies have equivalent performance. However it uses Bayesian reasoning to arrive at this conclusion.
However, Bayesian reasoning employs conditional probability which does not hold in it's standard form in QM. Then the question becomes if I have 2 search algorithms in QM do they have equivalent performance across all possible problems? Or in other words is No Free Lunch Theorem generalizable to Quantum Computation?
