Two new configurations of superposition of quantum states corresponding to the angular momentum of spin-1 quantum system is proposed in this article. One is a trivial state, |β, α⊥〉≡ (I −|α〉〈α|)|β〉, which consists of two Klauder’s type of spin coherent state |α〉 and |β〉 that is also perpendicular to |α〉, and the other is a non-trivial case composed of vector product of two different copies of spin states, |α〉 and |β, α⊥〉, i.e. |vps〉 := |α〉×|β, α⊥〉. Some properties of such quantum states are discussed. For instance, depending on the particular choice of parameters, we show that they minimize both the Heisenberg and Robertson-Schr\(\ddot {o}\)dinger uncertainty relations (RSUR) of each pair of the angular momentum components while the standard spin-coherent states do not satisfy. We have also shown that preparing the system state as a |β, α⊥〉 and choosing one of the mentioned orthogonal states, |vps〉, one can find a minimum lower bound for the Maccone-Pati uncertainty relations (MPUR) which is stronger than the other uncertainties. We also establish an irreducible and unitary representation of Lie algebra su(2) through the introduced states.

本文提出了对应于自旋 1 量子系统角动量的两种新的量子态叠加构型。一个是微不足道的状态，| β , α ⊥〉≡ ( I −| α〉〈α |)| β〉，由两个 Klauder 类型的自旋相干态组成 | α〉 和 | β〉 也垂直于 | α〉，另一个是由两个不同自旋态副本的向量积组成的非平凡情况，| α〉 和 | β , α ⊥>, 即 | v p s〉 := | α〉×| β , α ⊥>。讨论了这种量子态的一些性质。例如，根据参数的特定选择，我们表明它们最小化了每对角动量分量的 Heisenberg 和 Robertson-Schr \(\ddot {o}\) dinger 不确定性关系 (RSUR)，而标准自旋-相干状态不满足。我们还展示了将系统状态准备为 | β , α ⊥> 并选择上述正交状态之一，| v p小号〉，可以找到比其他不确定性更强的 Maccone-Pati 不确定性关系（MPUR）的最小下界。我们还通过引入的状态建立了李代数s u (2)的不可约和酉表示。