Quantum resource theories (QRTs) provide a comprehensive and practical framework for the analysis of diverse quantum phenomena. A fundamental task within QRTs is the quantification of resources inherent in a given quantum state. In this work, we introduce a unified computational framework for a class of widely utilized quantum resource measures, derived from convex roof extensions. We establish that the computation of these convex roof resource measures can be reformulated as an optimization problem over a Stiefel manifold, which can be further unconstrained through polar projection. Compared to existing methods employing semi-definite programming (SDP), gradient-based techniques or seesaw strategy, our approach not only demonstrates satisfying computational efficiency but also maintains applicability across various scenarios within a unified framework. We substantiate the efficacy of our method by applying it to several key quantum resources, including entanglement, coherence, and magic states. Moreover, our methodology can be readily extended to other convex roof quantities beyond the domain of resource theories, suggesting broad applicability in the realm of quantum information theory.

量子资源理论 （QRT） 为分析各种量子现象提供了一个全面而实用的框架。QRT 中的一项基本任务是量化给定量子态中固有的资源。在这项工作中，我们为一类广泛使用的量子资源度量引入了一个统一的计算框架，该度量源自凸屋顶扩展。我们确定这些凸顶资源度量的计算可以重新表述为 Stiefel 流形上的优化问题，该流形可以通过极投影进一步不受约束。与采用半定规划 （SDP）、基于梯度的技术或跷跷板策略的现有方法相比，我们的方法不仅展示了令人满意的计算效率，而且在统一的框架内保持了在各种场景中的适用性。我们通过将方法应用于几个关键的量子资源（包括纠缠、相干和魔态）来证实该方法的有效性。此外，我们的方法可以很容易地扩展到资源理论领域之外的其他凸屋顶量，这表明在量子信息论领域具有广泛的适用性。