Quantum constellations

01.01.2016, 00:00

Newsletter 9

Shortly before disappearing in mysterious circumstances at the age of 32, the Italian physicist Ettore Majorana invented a beautiful, yet largely ignored, representation of finite quantum systems. A pure state of spin S is expressed as a set of 2S points on the unit sphere: the Majorana constellation. This provides an intuitive method to study these systems from a purely geometric perspective. As a result, the Majorana representation has emerged as a most useful tool in many different fields. Spin coherent states are the most classical states, in the sense that they point "somewhere" as much as possible. The Majorana constellations for these states collapse to a single point. In this project, we attempt to characterize what states might serve as the opposite of coherent states. Such states, which point "nowhere", can be considered as the kings of quantumness. The associated Majorana constellation consists of a set of 2S points distributed in the "most symmetric" fashion over the sphere. This relates closely to other problems, such as Thomson’s or spherical t-designs. Apart from their indisputable geometrical beauty, there surely is plenty of room for applications of such states, the generation of which has started at MPL.

Contact: markus.grassl(at)mpl.mpg(dot)de
Group: Leuchs Division
Reference: G. Björk et al., Physical Review A 92, 031801(R) (2015).