Let me take Grover's algorithm as an example. In most cases, Grover's algorithm is able to yield with a high probability the desired term of the superposition. When the superposition has more than 4 terms, there's a small chance we will not obtain the desired term of the superposition, in which case we can repeat the procedure and measure it again, until we really get the desired result.
Although the probability of not getting the desired result decreases exponentially, it is technically not guaranteed that one will ever get the desired measurement. Therefore, we cannot prove that Grover's algorithm is an algorithm because we cannot prove it terminates with the correct answer in a finite number of steps. (Otherwise, what part of the definition of "algorithm" I'm missing here?)
We can however define Grover's algorithm as a Las Vegas algorithm because if we do not measure the desired result, we could produce a "failure" result, satisfying therefore the definition of "Las Vegas algorithm".
Surely a quantum computer is able to calculate everything a classical computer can, so quantum computers can execute algorithms in the formal sense of the word. But is there an algorithm (not a Las Vegas algorithm) that uses true quantum features like superpositions and entanglement always producing the right answer in a finite number of steps and is not a Las Vegas algorithm? That's what I'm after. I appreciate any light on this direction.