某些对称模和反模在部分迹前后的关系
Relations for certain symmetric norms and anti-norms before and after partial trace
摘要：
研究了部分迹运算下某些酉不变模和反模的变化。考虑的规范形成一个双参数的家庭，包括两个Ky范和Schatten规范作为特殊情况。所得结果涉及两个有限维Hilbert空间的张量积上的算子。对于任何这样的运营商，我们得到了相应的维数和范数的部分迹的范数的上界。对于正矩阵的某些反范数，得到了方向相反的类似不等式。通过Stinespring表示，结果被放在保迹完全正映射的上下文中。我们还得到了一个复合量子系统和它的一个子系统的统一熵之间的不等式，其中还涉及到示踪维数。
英文摘要：
Changes of some unitarily invariant norms and anti-norms under the operation of partial trace are examined. The norms considered form a two-parametric family, including both the Ky Fan and Schatten norms as particular cases. The obtained results concern operators acting on the tensor product of two finite-dimensional Hilbert spaces. For any such operator, we obtain upper bounds on norms of its partial trace in terms of the corresponding dimensionality and norms of this operator. Similar inequalities, but in the opposite direction, are obtained for certain anti-norms of positive matrices. Through the Stinespring representation, the results are put in the context of trace-preserving completely positive maps. We also derive inequalities between the unified entropies of a composite quantum system and one of its subsystems, where traced-out dimensionality is involved as well.
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