Frontiers of quantum physics

Abstract:

A comparison of the query complexity analysis of quantum algorithms was presented. Two different ways of representing a permutation in terms of a black box quantum oracle were provided. A simple promise problem that minimal quantum oracles could solve faster that the classical oracles was discussed. Results showed that the possibility of efficiently solving nonautomorphic graph isomorphism (NAGI) could be excluded by simulating a simpler oracle using standard oracle for a one-to-one function. © Oxford University Press 2002.

Abstract:

A scheme for demonstrating entanglement swapping using trapped Bose-Einstein condensates was presented. The swapping was accomplished by detection of the total number of atoms leaking out of two adjacent traps. The scheme was capable of being used for concentrating the entanglement shared between two parties in the form of entangled condensates.

Abstract:

A method of testing both Abelian and non-Abelian geometric phases for a general spin-J system modeled by two coupled Bose-Einstein condensates is proposed. The method allows to test geometric phases for spin values as mesoscopic as J∼104.

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.