Computing complexity measures for quantum states based on exponential   families
  Given a multiparticle quantum state, one may ask whether it can be represented as a thermal state of some Hamiltonian with k-particle interactions only. The distance from the exponential family defined by these thermal states can be considered as a measure of complexity of a given state. We investigate the resulting optimization problem and show how symmetries can be exploited to simplify the task of finding the nearest thermal state in a given exponential family. We also present an algorithm for the computation of the complexity measure and consider specific examples to demonstrate its applicability. 
S\"onke Niekamp, Tobias Galla, Matthias Kleinmann, Otfried G\"uhne
quant-ph cond-mat.stat-mech