Title: Global and local thermometry schemes in coupled quantum systems,
Abstract: We study the ultimate bounds on the estimation of temperature for an
interacting quantum system. We consider two coupled bosonic modes that are
assumed to be thermal and using quantum estimation theory establish the role
the Hamiltonian parameters play in thermometry. We show that in the case of a
conserved particle number the interaction between the modes leads to a decrease
in the overall sensitivity to temperature, while interestingly, if particle
exchange is allowed with the thermal bath the converse is true. We explain this
dichotomy by examining the energy spectra. Finally, we devise experimentally
implementable thermometry schemes that rely only on locally accessible
information from the total system, showing that almost Heisenberg limited
precision can still be achieved, and we address the (im)possibility for
multiparameter estimation in the system.