The information stored in quantum systems is much larger than that of classical systems. In classical physics, a combined system of N sub-systems (e.g., N bits) with m states each, has mN possible states, meaning that such a system can represent one integer number between 1 and mN. By contrast, a quantum system made of N sub-systems with m (orthogonal) states can simultaneously represent mN real numbers (or complex numbers if the time-evolution is factored out). Therefore quantum information can potentially revolutionize information technology.
I have led a study (Obreschkow et al. 2007) on how quantum information is stored in so-called quantum dots and developed the idea that polarons – the product states of electrons and phonons – can be described in a non-orthogonal basis in Hilbert space. This basis, called the natural basis, has the advantage that every basis state is easily described geometrically and that the polaron wave functions of the eigenstates can easily be calculated (see figure). I also had a chance to contribute to interesting studies on the controlled transport of quantum information across a one-dimensional spin chain (Bruderer et al. 2012), and on the reconstruction of quantum systems from a set of sparse measurements through so-called inverse counting statistics (Bruderer et al. 2014).
Statistics of irregular dice
You roll a six-sided die with parallel faces but non-equal edge lengths. What is the probability to land on each face? Little is known about the outcome statistics of these objects, and yet there are several important practical applications, from manufacturing (i.e. objects falling on conveyer belts) through to packing of granular material and proteins. To describe and understand the outcome statistics of irregular dice, I have initiated a multi-national research activity that includes analytical, experimental and computational efforts. Recently, we published a first series of experiments and an analytical theory based on Gibbs-distributions (Riemer et al. 2013). To strengthen the theoretical side of the project, I wrote a computer simulation of falling, bouncing and rolling irregular dice that can be downloaded here.