有限维可分性条件的Rényi和Tsallis公式
Rényi and Tsallis formulations of separability conditions in finite dimensions
摘要：
利用Rényi熵和Tsallis熵给出了有限维子系统的二分量子系统的可分性条件。熵的不确定性关系往往导致纠缠准则。我们提出了新的方法的基础上卷积的离散概率分布。根据卷积方案，对整个系统的测量由局部测量构成。基于Maassen-Uffink型的不确定关系和优控关系，导出了可分离性条件。在每个子系统上，我们使用一对次归一化向量，形成秩一POVM。我们还得到了具有特殊结构的局部测量的熵可分性条件，如相互无偏基和对称信息完全测量。导出的可分性条件的相关性证明了几个例子。
英文摘要：
Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of Rényi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach based on the convolution of discrete probability distributions. Measurements on a total system are constructed of local ones according to the convolution scheme. Separability conditions are derived on the base of uncertainty relations of the Maassen-Uffink type as well as majorization relations. On each of subsystems, we use a pair of sets of subnormalized vectors that form rank-one POVMs. We also obtain entropic separability conditions for local measurements with a special structure, such as mutually unbiased bases and symmetric informationally complete measurements. The relevance of the derived separability conditions is demonstrated with several examples.
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