Informational distance on quantum-state space
Informational distance on quantum-state space
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DOI：
10.1103/physreva.69.032106
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发表时间：
2004-03
影响因子：
2.9
通讯作者：
S. Luo;Qiang Zhang
中科院分区：
文献类型：
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作者：
S. Luo;Qiang Zhang
通过在概率密度空间上形式化地推广经典的Hellinger距离和亲和力，我们在由所有密度算符组成的量子态空间上引入了它们的量子模拟。我们证明了量子Hellinger距离的无穷小形式是Wigner和Yanase在1963年引入的倾斜信息。我们将Hellinger距离和亲和力与Bures距离和保真度进行了比较，并建立了它们的各种基本性质。我们进一步应用它们来刻画纠缠，并建立一些不寻常的不确定关系，这些关系与两个不同量子态中单个可观测到的不同时测量有关。
By formally generalizing the classical Hellinger distance and affinity on the space of probability densities, we introduce their quantum analog on the quantum state space consisting of all density operators. We show that the infinitesimal form of the quantum Hellinger distance is the skew information introduced by Wigner and Yanase in 1963. We compare the Hellinger distance and affinity with the Bures distance and fidelity, and establish a variety of their fundamental properties. We further apply them to characterizing entanglement and to establishing some unusual uncertainty relations relating nonsimultaneous measurements of a single observable in two different quantum states.