论文标题
紧凑的凸结构及其在持续结果测量的模拟，不兼容和凸资源理论中的应用
Compact convex structure of measurements and its applications to simulability, incompatibility, and convex resource theory of continuous-outcome measurements
论文作者
论文摘要
我们介绍了有关订单单位Banach Space $ e $与Banach Produal所描述的可能无限维度的一般概率理论的一般测量的后处理预订和等效关系。我们将测量空间$ \ mathfrak {m}（e）$定义为一组在$。$上定义$ \ mathfrak {m}（e）$上的弱拓扑的连续测量等效类别的等效类别，这是州对任何有限label em ne $ ne $ ne $ ne $ y y y y y y y y y y y y y y y y y y y y y y y y y y的最弱点，配备了与测量概率混合物相对应的凸操作，可以视为定期嵌入局部凸出的Hausdorff空间中的紧凑型凸。我们还证明，测量空间$ \ mathfrak {m}（e）$是无限维度的，除非系统为$ 1 $维度并给出后处理后处理单调仿射功能的表征。我们将这些一般结果应用于可模拟性和测量不兼容的问题。我们表明，与分别相对于可模拟或兼容测量值的稳健性测量与状态歧视概率的最佳比率相吻合。后一个不兼容测量结果的结果概括了有限维量子测量结果的最新结果。在整个论文中，可以系统地使用任何弱$ \ ast $连续测量的连续测量，可以在弱拓扑结构中任意近似。
We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the measurement space $\mathfrak{M}(E)$ as the set of post-processing equivalence classes of continuous measurements on $E .$ We define the weak topology on $\mathfrak{M} (E)$ as the weakest topology in which the state discrimination probabilities for any finite-label ensembles are continuous and show that $\mathfrak{M}(E)$ equipped with the convex operation corresponding to the probabilistic mixture of measurements can be regarded as a compact convex set regularly embedded in a locally convex Hausdorff space. We also prove that the measurement space $\mathfrak{M}(E) $ is infinite-dimensional except when the system is $1$-dimensional and give a characterization of the post-processing monotone affine functional. We apply these general results to the problems of simulability and incompatibility of measurements. We show that the robustness measures of unsimulability and incompatibility coincide with the optimal ratio of the state discrimination probability of measurement(s) relative to that of simulable or compatible measurements, respectively. The latter result for incompatible measurements generalizes the recent result for finite-dimensional quantum measurements. Throughout the paper, the fact that any weakly$\ast$ continuous measurement can be arbitrarily approximated in the weak topology by a post-processing increasing net of finite-outcome measurements is systematically used to reduce the discussions to finite-outcome cases.
