Quantifying stability of quantum statistical ensembles

We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble 'stable' if a small number of local measurements cannot significantly modify the total-energy distribution representing the ensemble. First, we numerically calculate the evolution of the stability measure introduced in our previous work Hahn and Fine (2016 Phys. Rev. E 94 062106) for an ensemble representing a mixture of two canonical ensembles with very different temperatures in a periodic chain of interacting spins-1/2. Second, we propose other possible stability measures and discuss their advantages and disadvantages. We also show that, for small system sizes available to numerical simulations of local measurements, finite-size effects are rather pronounced.