论文标题
通过几乎凸的量子熵量的连续性
Continuity of quantum entropic quantities via almost convexity
论文作者
论文摘要
根据Alicki，Fannes和Winter的条件熵连续性的证明，我们在这项工作中介绍了几乎本地仿射方法（Alaff）方法。这种方法使我们能够证明衍生熵数量的各种连续性界限。首先，我们将Alaff方法应用于叶藻相对熵。这样，我们恢复已知的几乎紧密的界限，但还为相对熵恢复了一些新的连续性界限。随后，我们将我们的方法应用于Belavkin-Staszewski相对熵（BS-Entropy）。对于BS条件熵，BS-Mutual和BS条件相互信息，这会产生新的明确界限。在途中，我们证明了叶片相对熵和BS-内向的几乎是凹度，这可能具有独立的关注。最后，我们在量子信息理论中的各种情况下显示了这些连续性界限的某些应用。
Based on the proofs of the continuity of the conditional entropy by Alicki, Fannes, and Winter, we introduce in this work the almost locally affine (ALAFF) method. This method allows us to prove a great variety of continuity bounds for the derived entropic quantities. First, we apply the ALAFF method to the Umegaki relative entropy. This way, we recover known almost tight bounds, but also some new continuity bounds for the relative entropy. Subsequently, we apply our method to the Belavkin-Staszewski relative entropy (BS-entropy). This yields novel explicit bounds in particular for the BS-conditional entropy, the BS-mutual and BS-conditional mutual information. On the way, we prove almost concavity for the Umegaki relative entropy and the BS-entropy, which might be of independent interest. We conclude by showing some applications of these continuity bounds in various contexts within quantum information theory.
