论文标题
Lipschitz的量子经典条件熵相对于角距离和相关特性
Lipschitz continuity of quantum-classical conditional entropies with respect to angular distance and related properties
论文作者
论文摘要
我们得出了与角度距离相对于量子古典条件熵结合的Lipschitz连续性，其Lipschitz常数与调节系统的尺寸无关。在某些情况下，这种界限比以前的连续性边界更明显，后者要么基于痕量距离（不可能的Lipschitz连续性），要么基于角度距离，但不包括调节系统。但是，我们发现界限并未直接推广到完全量子条件熵。为了研究这种情况下可能的反例，我们研究了饱和fuchs的表征 - van de graaf不等式，因此具有大约等于痕迹距离的角度距离。在可逆情况下，我们给出了此类状态的确切表征。对于不可避免的情况，我们表明这种情况似乎更加详尽，并且似乎与表征保留富裕度的测量值的问题密切相关。
We derive a Lipschitz continuity bound for quantum-classical conditional entropies with respect to angular distance, with a Lipschitz constant that is independent of the dimension of the conditioning system. This bound is sharper in some situations than previous continuity bounds, which were either based on trace distance (where Lipschitz continuity is not possible), or based on angular distance but did not include a conditioning system. However, we find that the bound does not directly generalize to fully quantum conditional entropies. To investigate possible counterexamples in that setting, we study the characterization of states which saturate the Fuchs--van de Graaf inequality and thus have angular distance approximately equal to trace distance. We give an exact characterization of such states in the invertible case. For the noninvertible case, we show that the situation appears to be significantly more elaborate, and seems to be strongly connected to the question of characterizing the set of fidelity-preserving measurements.
