论文标题
最佳协变量量子测量
Optimal covariant quantum measurements
论文作者
论文摘要
我们讨论对称量子测量和相关的协变量可观测值，分别建模为仪器和正操作员值衡量标准。这项工作的重点是测量值的最佳性能，即极端，信息完整性和Rank-1特性，将（Rank-1）投影值评估措施的互补类别对比。这项工作的前半部分仅集中于有限结果测量对称的W.R.T.我们使用这些Kraus-operator的协变量仪器的Kraus-Kraus-oserator进行了详尽的特征，并使用这些Kraus-operator来得出详尽的特征。我们通过表明可观察到的对称组的协方差包含与两种可观察到的互补优化类别的代表家族相关的协方差来激发协方差方法的使用，并表明即使是与等级-1投影值的略有偏差，也可以产生一个极端的信息完整的排名1。这项工作的后半部分为（可能）无限维度的连续测量得出了相似的结果。例如，我们研究协方差相空间仪器，其结构和极端性能。
We discuss symmetric quantum measurements and the associated covariant observables modelled, respectively, as instruments and positive-operator-valued measures. The emphasis of this work are the optimality properties of the measurements, namely, extremality, informational completeness, and the rank-1 property which contrast the complementary class of (rank-1) projection-valued measures. The first half of this work concentrates solely on finite-outcome measurements symmetric w.r.t. finite groups where we derive exhaustive characterizations for the pointwise Kraus-operators of covariant instruments and necessary and sufficient extremality conditions using these Kraus-operators. We motivate the use of covariance methods by showing that observables covariant with respect to symmetric groups contain a family of representatives from both of the complementary optimality classes of observables and show that even a slight deviation from a rank-1 projection-valued measure can yield an extreme informationally complete rank-1 observable. The latter half of this work derives similar results for continuous measurements in (possibly) infinite dimensions. As an example we study covariant phase space instruments, their structure, and extremality properties.
