几种量子测量的细粒度不确定关系
Fine-grained uncertainty relations for several quantum measurements
摘要：
研究了有限维希尔伯特空间中几种量子测量的细粒度不确定关系。所提出的方法是基于相应的正矩阵的谱范数的精确计算或估计。细粒度的不确定性关系的状态独立的形式推导出任意一组相互无偏基地。这样的关系与最近的概念相互无偏测量扩展。以类似的方式考虑所谓相互偏置基的情况。我们还讨论了制定细粒度的不确定性关系的情况下，广义测量。一般的方法，然后应用到两个测量有关的状态歧视。三秩一投影测量的情况下，进一步研究的细节。特别是，我们认为细粒度的不确定性关系的相互无偏基地在三维希尔伯特空间。
英文摘要：
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices. Fine-grained uncertainty relations of the state-independent form are derived for an arbitrary set of mutually unbiased bases. Such relations are extended with a recent notion of mutually unbiased measurements. The case of so-called mutually biased bases is considered in a similar manner. We also discuss a formulation of fine-grained uncertainty relations in the case of generalized measurements. The general approach is then applied to two measurements related to state discrimination. The case of three rank-one projective measurements is further examined in details. In particular, we consider fine-grained uncertainty relations for mutually unbiased bases in three-dimensional Hilbert space.
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