Computing complexity measures for quantum states based on exponential families
Sönke Niekamp, Tobias Galla, Matthias Kleinmann, Otfried Gühne · Journal of Physics A Mathematical and Theoretical · 2013
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.