MaxEnt principle and reduced density matrix estimation

Abstract

In this work we study the reduced density matrices of sublattices of fermionic, bosonic and spin lattice models. Firstly, we consider fermionic and bosonic lattice models, and we show that the reduced density matrix associated with a sublattice coincides with the state obtained by applying the maximum entropy principle under suitably chosen constraints. Secondly, for informationally incomplete scenarios, we considered spin lattice models. We study the performance of the MaxEnt method for estimating the reduced density matrix of sublattices of the lattice system. We find that the performance of the MaxEnt estimation improves not only with the number of measured observables (as expected), but also with the lattice length. In these cases, the MaxEnt solution can be considered, not as an exact solution, but as a good estimator.