Coauthors: Rajesh Pereira

Coherent states have been of interest since their discovery by Schrödinger in the 1920’s, being the most “classical” of all quantum states. In quantum information theory, one is often interested in states that display purely quantum phenomena, such as entanglement. To this end we discuss “anticoherent” spin states, those which do not mimic any classical behaviour. Using the Majorana representation we associate spin states with collections of points on the unit sphere. This beautifully illustrates the geometry of anticoherent states, which appear in very symmetrical configurations. These symmetries not only give an intriguing look into the most “quantum” spin states, they warrant the application to quantum information theory. We provide a wealth of new examples by relating anticoherence to spherical designs. Specifically, we show that spherical designs which are orbits of finite subgroups of O(3) correspond to anticoherent states. We also conjecture that anticoherent states maximize the well known geometric measure of entanglement, further illustrating their potential application.