论文标题
量子系统的概率模型，非上下文性不平等和噪声阈值中的概率模型中的不访问信息
Inaccessible information in probabilistic models of quantum systems, non-contextuality inequalities and noise thresholds for contextuality
论文作者
论文摘要
（嘈杂）量子系统的经典概率模型不仅与理解量子力学的非经典特征有关，而且它们也可用于确定将量子资源用于信息处理任务的可能优势。这些模型的一个共同特征是存在无法访问的信息的存在，如准备背景性概念所捕获的：相同密度操作员描述的量子状态的集合，因此在操作上无法区分，但在任何概率（本体论）模型中，应通过不同的概率分布来描述它们。在这项工作中，我们根据与任何一对具有相同密度运算符的合奏相关的概率分布的最大区分性来量化模型的无法访问信息，这是由分布的总变化距离量化的。从实验可测量的数量方面，我们在这种最大区分性方面获得了下限的家族。在理想量子的情况下，这会导致大约0.07的下限。这些界限也可以解释为新的强大准备性不平等不平等。我们的非上下文性不平等是根据最大旋转性熵和一般操作理论的痕量距离的概括来表达的，这可能具有独立的兴趣。 在足够强的噪声下，任何量子系统都会变为非上下文，即可以通过零无法访问信息的模型来描述。使用我们的非上下文性不等式，我们表明，只有当噪声通道的平均门忠诚度小于或等于1/d（1+1/2+...+1/d）时，这才能发生，其中d是希尔伯特空间的维度。
Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources for information processing tasks. A common feature of these models is the presence of inaccessible information, as captured by the concept of preparation contextuality: There are ensembles of quantum states described by the same density operator, and hence operationally indistinguishable, and yet in any probabilistic (ontological) model, they should be described by distinct probability distributions. In this work, we quantify the inaccessible information of a model in terms of the maximum distinguishability of probability distributions associated to any pair of ensembles with identical density operators, as quantified by the total variation distance of the distributions. We obtain a family of lower bounds on this maximum distinguishability in terms of experimentally measurable quantities. In the case of an ideal qubit this leads to a lower bound of, approximately, 0.07. These bounds can also be interpreted as a new class of robust preparation non-contextuality inequalities. Our non-contextuality inequalities are phrased in terms of generalizations of max-relative entropy and trace distance for general operational theories, which could be of independent interest. Under sufficiently strong noise any quantum system becomes preparation non-contextual, i.e., can be described by models with zero inaccessible information. Using our non-contextuality inequalities, we show that this can happen only if the noise channel has the average gate fidelity less than or equal to 1/D(1+1/2+...+1/D), where D is the dimension of the Hilbert space.
