Error Bounds for Open Quantum Systems with Harmonic Bosonic Bath

We investigate the dependence of physical observable of open quantum systems with Bosonic bath on the bath correlation function. We provide an error estimate of the difference of physical observable induced by the variation of bath correlation function, based on diagrammatic and combinatorial arguments. This gives a mathematically rigorous justification of the result in [Mascherpa et al, Phys Rev Lett 2017].