Approximation Methods for Analysis of Rate Equations

R. L. Ingraham

Rémi Robin, Pierre Rouchon

This paper analyzes the numerical approximation of the Lindblad master equation on infinite-dimensional Hilbert spaces. We employ a classical Galerkin approach for spatial discretization and investigate the convergence of the discretized solution to the exact solution. Using \textit{a priori} estimates, we derive explicit convergence rates and demonstrate the effectiveness of our method through examples motivated by autonomous quantum error correction.

Lee W. Casperson

The rate-equation approximation is one of the most fundamental and universally employed simplifications in laser analyses. The accuracy and regions of applicability of this approximation are explored in comparisons with more rigorous semiclassical models. Higher-order rate-equation approximations are also developed, and these improved models can yield much better accuracy than conventional rate equations with little added complexity. The modified adiabatic elimination methods reported here would also be useful in reducing the mathematical models governing other physical systems.

John A. Happel

Kohdai Kuroiwa, Debbie Leung

In this paper we propose a protocol for a data compression task, blind quantum data compression, with finite local approximations. The rate of blind data compression is susceptible to approximations even when the approximations are diminutive. This instability originates from the sensitivity of a structure of quantum states against approximations, which makes the analysis of blind compression in the presence of approximations intractable. In this paper we construct a protocol that takes advantage of the instability to reduce the compression rate substantially. Our protocol shows a significant reduction in rate for specific examples we examine. Moreover, we apply our methods to diagonal states and propose two types of approximation methods in this special case. We perform numerical experiments and observe that one of these two approximation methods performs significantly better than the other. Thus, our analysis makes a step toward general investigation of blind quantum data compression with the allowance of approximations towards further investigation of approximation-rate trade-off of blind quantum data compression.