来自统计比较理论的完全量子第二定律式陈述
Fully quantum second-law--like statements from the theory of statistical comparisons
摘要：
在广义资源理论中，人们的目标是将决定两个给定状态$ρ$和$σ$之间是否存在合适的转换（通常是保持理论的吉布斯状态的转换）的问题重新表述为检查一组类似第二定律的不等式是否成立的问题。这些初步说明的目的是说明统计比较理论（在布莱克威尔、勒卡姆和托格森的意义上）在这种情况下是如何有用的。特别是，我们提出了一个建设，其中第二定律制定一个合适的条件最小熵。虽然也给出了一般的全量子结果，但对于量子比特的情况以及$σ$与Gibbs态交换的情况，得到了更强的结果。
英文摘要：
In generalized resource theories, one aims to reformulate the problem of deciding whether a suitable transition (typically a transition that preserves the Gibbs state of the theory) between two given states $ρ$ and $σ$ exists or not, into the problem of checking whether a set of second-law--like inequalities hold or not. The aim of these preliminary notes is to show how the theory of statistical comparisons (in the sense of Blackwell, LeCam, and Torgersen) can be useful in such scenarios. In particular, we propose one construction, in which the second laws are formulated in terms of a suitable conditional min-entropy. Though a general, fully quantum result is also presented, stronger results are obtained for the case of qubits, and the case of $σ$ commuting with the Gibbs state.
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