Time evolution of coupled spin systems in a generalized Wigner   representation
  Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum optics and beyond. Continuous phase spaces have also been studied for finite-dimensional quantum systems such as spin systems. However, much less is known for finite-dimensional, coupled systems, and we present a complete theory of Wigner functions for this case. In particular, we provide a self-contained Wigner formalism for describing and predicting the time evolution of coupled spins which lends itself to visualizing the high-dimensional structure of multi-partite quantum states. We completely treat the case of an arbitrary number of coupled spins 1/2, thereby establishing the equation of motion using Wigner functions. The explicit form of the time evolution is then calculated for up to three spins 1/2. The underlying physical principles of our Wigner representations for coupled spin systems are illustrated with multiple examples which are easily translatable to other experimental scenarios. 
B\'alint Koczor, Robert Zeier, Steffen J. Glaser
quant-ph