Prof Vlatko Vedral FInstP

Abstract:

We discuss the question of the existence of quantum one-way permutations. First, we consider the question: if a state is difficult to prepare, is the reflection operator about that state difficult to construct? By revisiting Grover's algorithm, we present the relationship between this question and the existence of quantum one-way permutations. Next, we prove the equivalence between inverting a permutation and that of constructing polynomial size quantum networks for reflection operators about a class of quantum states. We will consider both the worst case and the average case complexity scenarios for this problem. Moreover, we compare our method to Grover's algorithm and discuss possible applications of our results.

Abstract:

The role of indistinguishability and particle statistics in a simple information processing scenario was analyzed. A different setting in which particle paths were locally mixed without any interaction of the internal degree of freedom with anything else was introduced. It was observed that for a given path selection one type of particles exhibited some entanglement in the internal degrees of freedom whereas the other exhibited none.