One-Way Ticket to Las Vegas and the Quantum Adversary

Abstract

We propose a new definition of quantum Las Vegas query complexity. We show that it is exactly equal to the quantum adversary bound. This is achieved by a new and very simple way of transforming a feasible solution to the adversary optimisation problem into a quantum query algorithm. This allows us to generalise the bound to include unidirectional access, multiple input oracles, and input oracles that are not unitary. As an application, we demonstrate a separation between unidirectional and bidirectional access to an input oracle for a rather natural unitary permutation inversion problem.

One Weird Trick Tightens the Quantum Adversary Bound, Especially for Success Probability Close to $1/2$

“…in [9]). But similarly to the universal query algorithm of [3,9], it turned out to be fruitful to think about both the "Gram matrix picture" and the "states-and-unitaries picture", using the latter to change the Gram matrices under consideration to more convenient ones. In our case, the convenience came from the perfect distinguishability of the modified final states, which corresponds to Gram matrices whose entries are exactly 0.…”