AI 中文总结
该研究建立量子资源理论与概率论的联系，证明资源度量强单调性对应资源为上鞅，利用鞅相关定理推导后选择等策略的效率界，揭示条件态渐近动力学的资源消失或冻结现象。
AI 中文摘要
我们在自由操作的重复应用下，建立了量子资源理论与概率论之间的联系。我们证明资源度量的强单调性意味着该资源是一个上鞅。随后，我们利用可选停时定理和鞅收敛定理推导后选择及其他自由自适应策略的效率界。我们还描述了条件态的渐近动力学，其中资源波动必然不存在，表明会出现两种不同现象之一：资源消失或资源冻结。
英文摘要
We establish a connection between quantum resource theory and probability theory, under repeated application of free operations. We show that strong monotonicity of a resource measure implies that the resource is a supermartingale. We then use the optional stopping and martingale convergence theorems to derive bounds on the efficiency of post-selection, and other free adaptive strategies. We also describe the asymptotic dynamics of the conditional state, where resource fluctuations are necessarily absent, showing one of two distinct phenomena occurs: resource vanishing or resource freezing.
Comments5 pages, 3 figures (+ 2 pages, 1 figure of Appendix + 8 pages of Supp. Mat.)
