可分离观测多参数估计的Nagaoka-Hayashi界的有效计算
Efficient computation of the Nagaoka--Hayashi bound for multi-parameter estimation with separable measurements
摘要：
在量子多参数计量中，寻找最佳的可达到的精度是一个重要的问题。解决这个问题的一种方法是计算边界，它限制了我们对某些物理量的估计精度。一个这样的界是Holevo Cramer Rao界的痕迹的均方误差矩阵。Holevo界是一个渐近可实现的边界时，允许任何测量策略，包括集体测量的许多副本的探针。在这项工作中，我们引入了一个更严格的边界，同时估计多个参数时，执行可分离的测量有限的副本的探针。这使得它在实验可及性方面更加相关。我们表明，这个界可以有效地计算铸造它作为一个半定的计划。我们说明了我们的约束与几个例子的集体测量有限副本的探头。这些结果的必要要求，以饱和的Holevo约束的影响。
英文摘要：
Finding the optimal attainable precisions in quantum multiparameter metrology is a non trivial problem. One approach to tackling this problem involves the computation of bounds which impose limits on how accurately we can estimate certain physical quantities. One such bound is the Holevo Cramer Rao bound on the trace of the mean squared error matrix. The Holevo bound is an asymptotically achievable bound when one allows for any measurement strategy, including collective measurements on many copies of the probe. In this work we introduce a tighter bound for estimating multiple parameters simultaneously when performing separable measurements on finite copies of the probe. This makes it more relevant in terms of experimental accessibility. We show that this bound can be efficiently computed by casting it as a semidefinite program. We illustrate our bound with several examples of collective measurements on finite copies of the probe. These results have implications for the necessary requirements to saturate the Holevo bound.
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