Dragomir Djokovic

Entangled states

Dragomir Djokovic retired in September 2006, but his passion for mathematics is stronger than ever. Dragomir has focused on the study of Lie Algebras, Lie Groups and in particular Classical Groups. Lie Groups describe the symmetry of structures and Dragomir uses this foundation for exploring a new subject.

“In the last few years, I got interested in quantum information theory and quantum computing. Essentially, we have a compact Lie group acting on a set of states of a multipartite quantum system, so I have been using my expertise in geometry and algebra to look at the spaces of such quantum systems. We consider the local unitary group (of qubits, for example) acting on a space and we want to understand and classify its orbits.” One of Dragomir’s recent interests is classifying entangled states of multipartite quantum system. “It’s surprising how quickly the problem becomes intractable. I worked with an undergraduate student (O. Chterental) examining pure states of four qubits. We can classify the orbits of a four-qubit system, but not five – the dimensionality is too high, it’s too complicated.”

Orbits represent types of states of the quantum system. Finding adequate measures of the entanglement properties of such complex systems is essential for the construction of quantum computers.

The leap to quantum information theory was not difficult for Dragomir. “I’m a novice in this area of research,” he comments. “But I’m using the same tools. Computing has always been an essential component of my research, so it’s natural for me to be interested in quantum computing and what it might accomplish.”

Dragomir continues to pursue questions in quantum information theory, orthogonal groups and invariant theory.

University of Waterloo Mathematics, Annual Report 2006