Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the methods are limited by computational resources and the efficiency and accuracy of the underlying algorithms for convex optimization. We derive a stable reformulation of the convex nonlinear semidefinite programming, SDP, model for the key rate calculation problems. We use this to develop an efficient, accurate algorithm. The stable reformulation is based on novel forms of facial reduction, FR, for both the linear constraints and nonlinear quantum relative entropy objective function. This allows for a Gauss-Newton type interior-point approach that avoids the need for perturbations to obtain strict feasibility, a technique currently used in the literature. The result is high accuracy solutions with theoretically proven lower bounds for the original QKD from the FR stable reformulation. This provides novel contributions for FR for general SDP. We report on empirical results that dramatically improve on speed and accuracy, as well as solving previously intractable problems.

中文翻译：

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量子密钥分配率计算的鲁棒内点法

基于数字密钥率计算问题的量子密钥分发安全证明方法 QKD 原则上是强大的。然而，这些方法的实用性受到计算资源和凸优化底层算法的效率和准确性的限制。我们为关键速率计算问题推导出凸非线性半定规划 SDP 模型的稳定重构。我们用它来开发一种高效、准确的算法。对于线性约束和非线性量子相对熵目标函数，稳定的重构基于新形式的面部缩减 FR。这允许采用高斯-牛顿型内点方法，避免需要扰动以获得严格的可行性，这是目前文献中使用的一种技术。结果是具有理论上证明的来自 FR 稳定重构的原始 QKD 的下限的高精度解决方案。这为通用 SDP 的 FR 提供了新的贡献。我们报告的实证结果显着提高了速度和准确性，并解决了以前难以解决的问题。