André Berthiaume

Quantum secret sharing

Secret sharing is a procedure for splitting a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. We show how this procedure can be implemented using Greenberger-Horne-Zeilinger (GHZ) states. In the quantum case the presence of an eavesdropper will introduce errors so that his presence can be detected. We also show how GHZ states can be used to split quantum information into two parts so that both parts are necessary to reconstruct the original qubit.

Quantum Kolmogorov Complexity

In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the amount of innate randomness (or information) contained in the string. We define the quantum Kolmogorov complexity of a qubit string as the length of the shortest quantum input to a universal quantum Turing machine that produces the initial qubit string with high fidelity. The definition of P. Vitanyi (2001, IEEE Trans. Inform. Theory47, 2464?2479) measures the amount of classical information, whereas we consider the amount of quantum information in a qubit string. We argue that our definition is a natural and accurate representation of the amount of quantum information contained in a quantum state. Recently, P. Gacs (2001, J. Phys. A: Mathematical and General34, 6859?6880) also proposed two measures of quantum algorithmic entropy which are based on the existence of a universal semidensity matrix. The latter definitions are related to Vitanyis and the one presented in this article, respectively.

Bounding the firing synchronization problem on a ring

In this paper we improve the upper and lower bounds on the complexity of solutions to the firing synchronization problem on a ring. In this variant of the firing synchronization problem the goal is to synchronize a ring of identical finite automata. Initially, all automata are in the same state except for one automaton that is designated as the initiator for the synchronization. The goal is to define the set of states and the transition function for the automata so that all machines enter a special fire state for the first time and simultaneously during the final round of the computation. In our work we present two solutions to the ring firing synchronization problem, an 8-state minimal-time solution and a 6-state non-minimal-time solution. Both solutions use fewer states than the previous best-known minimal-time automaton, a 16-state solution due to Culik. We also give the first lower bounds on the number of states needed for solutions to the ring firing synchronization problem. We show that there is no 3-state solution and no 4-state, symmetric, minimal-time solution for the ring.

A hybrid approach to projects in gaming courses

We describe an approach to projects used in game development courses that supports learning individual skills while also developing team skills. Early assignments focus on developing individual skills in coding and content creation, and when those skills are honed, students form teams to work on a larger and more complex game. Classes that use a hybrid approach, that is individual projects that build toward a large group project, allow students to solidly learn game development skills required of gaming graduates and yet stimulate creativity and challenge students to move beyond their comfort zone.

Supporting therapists in motion-based gaming for brain injury rehabilitation

In this paper, we describe a work-in-progress that involves therapists who use commercial motion-based video games (e.g. Wii) in therapies involving patients who have had a brain injury (BI). We are collecting data to inform a case-based recommender (CBR) system that will help therapists stay current and choose appropriate motion-games for their patients. Data from the CBR system will (1) establish commercial motion-game efficacy among a larger and more diverse BI patient population than in previous work and (2) inform custom games that better meet needs for BI therapies.