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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Notes on general SIC-POVMs
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Notes on general SIC-POVMs

机译：常规SIC-POVM的注意事项

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摘要

An unavoidable task in quantum information processing is how to obtain data about the state of an individual system by suitable measurements. Informationally complete measurements are relevant in quantum state tomography, quantum cryptography, quantum cloning, and other questions. Symmetric informationally complete measurements (SIC-POVMs) form an especially important class of such measurements. We formulate some novel properties and relations for general SIC-POVMs in a finite-dimensional Hilbert space. For a given density matrix and any general SIC-POVM, the so-called index of coincidence of generated probability distribution is exactly calculated. Using this result, we obtain state-dependent entropic bounds for a single general SIC-POVM. Lower entropic bounds are derived in terms of the Rényi α-entropies for α∈[2;∞) and the Tsallis α-entropies for α ∈ (0; 2]. A lower bound on the min-entropy of an SIC-POVM is separately examined. For a pair of general SIC-POVMs, entropic uncertainty relations of the Maassen–Uffink type are considered.
机译：量子信息处理中不可避免的任务是如何通过适当的测量获得有关单个系统状态的数据。信息完整的测量与量子状态层析成像，量子密码术，量子克隆和其他问题有关。对称的信息完整测量（SIC-POVM）构成了此类测量的一个特别重要的类别。我们在有限维希尔伯特空间中为一般SIC-POVM制定了一些新颖的性质和关系。对于给定的密度矩阵和任何常规的SIC-POVM，将精确计算生成的概率分布的所谓一致性指数。使用此结果，我们获得了单个通用SIC-POVM的状态依赖熵范围。根据α∈[2;∞）的Rényiα熵和α∈（0; 2]的Tsallisα熵得出下熵边界。SIC-POVM的最小熵的下界为对于一对通用的SIC-POVM，考虑了Maassen-Uffink类型的熵不确定性关系。

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