Computing devices must be implemented using physical devices. The computing industry continually strives for smaller and faster computational devices. Ultimately the physics of these devices must be described by quantum mechanics. It has been shown that certain problems can only be solved using a quantum computer. Furthermore, there are classes of problems which can be solved exponentially faster (expected time) using quantum computer algorithms than any known classical algorithm.
One of the essential features of quantum computation which is used to improve over the classical is entanglement. Entanglement illustrates the nonlocal behaviour of quantum mechanics. We are investigating measures of entanglement and criteria for separability. We are also working in quantum communication complexity, which considers the amount of information which needs to be communicated to solve certain problems. Entanglement can aid communication for certain problems. A related topic is the simulation of entanglement.
We are investigating the relationships between the Shannon and von Neumann entropy and the classical and quantum expected communication complexity. We are also interested in the relation between exact and expected communication complexity in terms of rank and the above-mentioned measures of entropy.