对于所有的量子态，什么时候一个可观测量的方差小于或等于另一个的方差？
When is the variance of one observable less than or equal to that of another with respect to all quantum states?
摘要：
在量子力学中，著名的Loewner序表示一个可观察量的期望值对于所有量子态都小于或等于另一个可观察量的期望值。本文提出并研究了一个用方差表示的相似序关系，并证明了两个定理。我们的第一个结果指出，一个可观察量的方差是小于或等于另一个关于所有的量子态的当且仅当前者是后者的$1$ -Lipschitz函数。另一个主要结果，我们证明的特点，顺序自同构关于这个建议的顺序关系。事实证明，在某种意义上，这些自同构有一个更严格的形式比在Loewner秩序的情况下。
英文摘要：
In quantum mechanics, the well-known Loewner order expresses that one observable's expectation value is less than or equal than that of another with respect to all quantum states. In this paper we propose and study a similar order relation in terms of the variance, and we prove two theorems. Our first result states that one observable's variance is less than or equal than that of another with respect to all quantum states if and only if the former is a $1$-Lipschitz function of the latter. The other main result we prove characterises the order automorphisms with respect to this proposed order relation. It turns out that in some sense these automorphisms have a more rigid form than in the case of the Loewner order.
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