论文标题
鉴于弱价值的不确定性关系
Uncertainty Relations of Variances in View of the Weak Value
论文作者
论文摘要
已知Schr {Ö} dinger不平等是Kennard-Robertson不平等的基础，这是两种可观察到的$ a $ a $ a $ a和$ b $乘积的量子不确定性的标准表达，因为后者是从前者派生的。在本文中，我们指出，尽管更微妙，但还有另一种不平等，它是schr {Ö} dinger不平等的基础。该观察结果的关键组成部分是使用弱值运算符$ a _ {\ rm w}（b）$在我们以前的作品中引入的$（以Aharonov的弱价值命名），该$在测量$ b $时被证明是$ a $ a $的代理操作员。我们新颖的不平等的下限补充了Schr {Ö} dinger不等式的术语，该术语表示$ a _ {\ rm w}（b）$和$ a $之间的不和谐。此外，更仔细地研究了Schr {Ö} dinger不等式的分解，这也是我们以前的作品中通过使用弱值操作员来获得的，以分析其结构和最小的不确定性状态。我们的结果用一些基本旋转1和3/2型号进行了例证，$ a $ a $ a和$ b $的熟悉情况是粒子的位置和动力。
The Schr{ö}dinger inequality is known to underlie the Kennard-Robertson inequality, which is the standard expression of quantum uncertainty for the product of variances of two observables $A$ and $B$, in the sense that the latter is derived from the former. In this paper we point out that, albeit more subtle, there is yet another inequality which underlies the Schr{ö}dinger inequality in the same sense. The key component of this observation is the use of the weak-value operator $A_{\rm w}(B)$ introduced in our previous works (named after Aharonov's weak value), which was shown to act as the proxy operator for $A$ when $B$ is measured. The lower bound of our novel inequality supplements that of the Schr{ö}dinger inequality by a term representing the discord between $A_{\rm w}(B)$ and $A$. In addition, the decomposition of the Schr{ö}dinger inequality, which was also obtained in our previous works by making use the weak-value operator, is examined more closely to analyze its structure and the minimal uncertainty states. Our results are exemplified with some elementary spin 1 and 3/2 models as well as the familiar case of $A$ and $B$ being the position and momentum of a particle.
