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Description
Quantum master equations are widely used to describe the dynamics of open quantum systems. Among them, the Redfield equation provides high accuracy but may generate unphysical time evolution because it does not preserve positivity. To overcome this issue, the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation, which generates completely positive and trace preserving (CPTP) dynamics, has been utilized in a wide range of fields, including quantum information, condensed matter physics, and quantum optics. However, rigorous error bounds for the deviation of the GKSL equation from the exact dynamics have been established only in the short-time regime.
In this work, we propose a unified framework, called temporal coarse graining, for describing the approximations used to derive GKSL equations from the Redfield equation. We show that several representative approximations proposed in previous studies are included in this framework. Furthermore, we derive an upper bound on the difference between the time evolutions generated by the GKSL and Redfield equations and prove that this error remains uniformly bounded in time. As a result, we provide a rigorous long-time accuracy guarantee for GKSL equations describing finite open quantum systems.