This workshop has arisen from the need and desire of experimentalists working toward implementations of various quantum information processing tasks to interact with mathematicians on the one hand, and mathematicians working in quantum information or on its periphery to participate in attempts to implement quantum computation and communication technologies on the other. Thus, by its very nature this workshop is heavily interdisciplinary. It is hoped that this event, held at the Institute for Quantum Computing in Waterloo, will lead to collaborations between scientists that would not have had the opportunity to interact otherwise. Some potential interaction points are discussed below.

Experimental quantum information aims to develop physical systems that can exhibit the requisite quantum properties as well as methods for controlling and characterizing these systems. This is a very challenging task that involves significant mathematical and statistical issues. Quantum properties, such as entanglement and superposition, are notoriously fragile. To harness these properties, two seemingly contradictory constraints are required: the systems must be completely isolated from their environment to fight decoherence, yet amenable to precise and rapid control by outside forces. Despite these constraints, several physical systems are being intensively investigated and rapid progress has been achieved over the last several years.

For example, entanglement is a critical quantum resource in most quantum information applications. Experiments with trapped ions have demonstrated 6 and 8 ion entangled states, where the 6 ion states have been used for quantum-enhanced phase measurements. Optical experiments have demonstrated key entangled states, known as graph states, in up to 6 optical photons. Nuclear magnetic resonance (NMR) experiments have demonstrated the production of 12 qubit pseudo-pure states; and recently a pair of superconducting qubits has, for the first time, been entangled. Key quantum logic gates and even small quantum computing algorithms have been demonstrated in several of these systems.

Quantum cryptography is arguably the most advanced quantum technology. This particular technology is dominated by optical implementations since photons can be distributed over large distances with low decoherence. Driven by improvements in entangled-photon source and detector technologies, quantum key distribution has been demonstrated over 100km in both fibre and free-space quantum channels. Several important questions remain in the theory of quantum cryptography and will have important consequences for the technology. Quantum key distribution has been shown to be secure under, as of yet, unrealistic conditions. Can we develop a working experimental system and prove that it is unconditionally secure even with all of its real world imperfections? Quantum key distribution systems can only tolerate a certain amount of errors before their security is potentially compromised. However, there remains a gap between the error rate of known secure systems and systems which we know are not secure. Can we develop protocols to close this gap and yield systems which are able to tolerate higher error rates, or achieve higher bit rates?