量子信息理论中的希尔伯特投影度规
Hilbert's projective metric in quantum information theory
摘要：
我们在量子信息理论的背景下引入和应用希尔伯特投影度量。度量是由凸锥，如集的积极，可分离或PPT运营商。它提供了量子态的统计可分辨性的度量以及在LOCC协议或其他保锥操作下纠缠减少的界。结果用一般锥和基模表示，并得到了量子信道的收缩性界，例如改进了Ruskai的迹模收缩不等式.给出了可拓性测度与基范数之间的一种新的对偶关系。对于两个给定的量子态对，我们证明了希尔伯特的投影度量的收缩是必要的和充分的概率量子操作的存在，映射到另一对。证明了Hilbert射影度量与Besloff界、保真度和各种范数之间的不等式。
英文摘要：
We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical distinguishability of quantum states and on the decrease of entanglement under LOCC protocols or other cone-preserving operations. The results are formulated in terms of general cones and base norms and lead to contractivity bounds for quantum channels, for instance improving Ruskai's trace-norm contraction inequality. A new duality between distinguishability measures and base norms is provided. For two given pairs of quantum states we show that the contraction of Hilbert's projective metric is necessary and sufficient for the existence of a probabilistic quantum operation that maps one pair onto the other. Inequalities between Hilbert's projective metric and the Chernoff bound, the fidelity and various norms are proven.
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