A geometric approach to study quantum entanglement is advocated. We discuss first the geometry of the set of mixed quantum states acting on a finite dimensional Hilbert space. Next we consider bipartite quantum system and analyze the set containing separable mixed states. Studying geometric properties of this set contributes to our understanding of quantum entanglement and its time evolution. Vulnerability of entanglement due to quantum noise and destruction of quantum information due to interaction with an environment form key questions concerning feasibility of quantum computers.
Karol Å»yczkowski was born in 1960 in Cracow, Poland. He is a theoretical physicist with diverse interests: classical and quantum chaos, nonlinear dynamics, foundations of quantum theory, quantum information processing, random matrices, applied mathematics and theory of voting. He has held a Humboldt Fellowship at the University of Essen (Germany) a Fulbright Fellowship at University of Maryland and has been a visiting researcher at the Perimeter Institute, Waterloo, Canada. Currently he is professor of Physics at Smoluchowski Institute of Physics, Jagiellonian University (Cracow) and Center for Theoretical Physics Polish Academy of Sciences (Warsaw). Co-author of the book Geometry of Quantum States published in 2006 by Cambridge University Press.