论文标题
旋转式挤压状态在Bloch四曲blo子上
Spin-entangled Squeezed State on a Bloch Four-hyperboloid
论文作者
论文摘要
Bloch倍曲底$ H^2 $是原始$ SO（2,1）$挤压状态的量子几何形状的基础。在\ cite {hasebe-2019}中，作者使用了非紧凑型霍普夫地图和bloch四摩托$ h^{2,2} $来探索挤压状态的$（2,3）$扩展。在本文中，我们进一步提出了基于另一个Bloch四摩托$ H^4 $的$（4,1）$版本的$（4,1）$版本的想法。我们表明，获得的$ SO（4,1）$挤压真空吸尘器是一种特定的四模式挤压状态，与以前的$（2,3）$挤压真空不一样。鉴于Schwinger的角度动量的表述，$ SO（4,1）$挤压真空被解释为所有整数旋转的无限数量最大纠缠的旋转对双方的叠加。我们阐明了$ SO（4,1）$挤压真空的基本特性，例如von Neumann的旋转纠缠，旋转相关性和不确定性关系，重点是它们对原始$ SO（2,1）$案例的区分。
The Bloch hyperboloid $H^2$ underlies the quantum geometry of the original $SO(2,1)$ squeezed states. In \cite{Hasebe-2019}, the author utilized a non-compact 2nd Hopf map and a Bloch four-hyperboloid $H^{2,2}$ to explore an $SO(2,3)$ extension of the squeezed states. In the present paper, we further pursue the idea to derive an $SO(4,1)$ version of squeezed vacuum based on the other Bloch four-hyperboloid $H^4$. We show that the obtained $SO(4,1)$ squeezed vacuum is a particular four-mode squeezed state not quite similar to the previous $SO(2,3)$ squeezed vacuum. In view of the Schwinger's formulation of angular momentum, the $SO(4,1)$ squeezed vacuum is interpreted as a superposition of an infinite number of maximally entangled spin-pairs of all integer spins. We clarify basic properties of the $SO(4,1)$ squeezed vacuum, such as von Neumann entropy of spin entanglement, spin correlations and uncertainty relations with emphasis on their distinctions to the original $SO(2,1)$ case.
