Daniel Burgarth of Friedrich-Alexander-Universität Erlangen-Nürnberg, alongside colleagues, has derived a bound quantifying error in the evolution of open quantum systems. This work establishes a way to measure error without relying on simplifying assumptions often used in quantum calculations.
The researchers demonstrate an explicit upper bound on the error of the rotating-wave approximation, even when accounting for energy loss and environmental interactions; this concept is visually represented by the narrow band of error remaining after averaging rapid oscillations, much like the trail of a spinning top. The findings apply to the strong-coupling limit and refine the derivation of the Gorini-Kossakowski-Lindblad-Sudarshan master equation from the Redfield master equation.
Nonperturbative Bounds on Open Quantum System Evolution
A mathematical framework for understanding how much deviation to expect when modeling complex quantum processes has been developed. This result can be employed to provide an explicit upper bound on the error of the rotating-wave approximation in the presence of dissipation and decoherence. The researchers applied the derived bound to scenarios involving strong coupling, where interactions between the system and its environment are particularly intense.
The GKLS form is often derived from the Redfield master equation using the secular approximation. This new work provides a way to rigorously assess the validity of that step. By consistently including noise within the mathematical framework, the team developed a method for treating it accurately, allowing it to remain unchanged when unaffected by the rotation, but requiring averaging within the rotating frame when it is.
The approach extends to situations in which the fast dynamics itself involves dissipation, while also quantifying the cost of the secular approximation, a standard step in deriving physically consistent equations for open quantum systems. The researchers write that by including the noise in the same framework, they obtain a prescription for treating it consistently, highlighting the practical benefit of their approach.
Rotating-Wave Approximation Error and Secular Approximation Limits
A newly derived mathematical bound quantifies the error inherent in approximating the behavior of open quantum systems, offering a tool applicable even when those systems strongly interact with their environment. The team demonstrated that the error remains confined within a “narrow band,” the width of which is determined by the newly established bound. Burgarth, Facchi, Gramegna, and Yuasa also cite previous work by Hu on the consistency and applicability of the rotating-wave approximation for open quantum systems, and by Benatti, Chruściński and Floreanini on local entanglement generation with Redfield dynamics.
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