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Given a multiparticle quantum state, one may ask whether it can berepresented as a thermal state of some Hamiltonian with k-particle interactionsonly. The distance from the exponential family defined by these thermal statescan be considered as a measure of complexity of a given state. We investigatethe resulting optimization problem and show how symmetries can be exploited tosimplify the task of finding the nearest thermal state in a given exponentialfamily. We also present an algorithm for the computation of the complexitymeasure and consider specific examples to demonstrate its applicability.

Computing complexity measures for quantum states based on exponential families