The classical and quantum dynamics of two particles constrained on \(S^1\) is discussed via Dirac’s approach. We show that when state is maximally entangled between two subsystems, the product of dispersion in the measurement reduces. We also quantify the upper bound on the external field \(\vec {B}\) such that \(\vec {B}\ge \vec {B}_{upper }\) implies no reduction in the product of dispersion pertaining to one subsystem. Further, we report on the cut-off value of the external field \(\vec {B}_{cutoff }\), above which the bipartite entanglement is lost and there exists a direct relationship between uncertainty of the composite system and the external field. We note that, in this framework it is possible to tune the external field for entanglement/unentanglement of a bipartite system. Finally, we show that the additional terms arising in the quantum Hamiltonian, due to the requirement of Hermiticity of operators, produce a shift in the energy of the system.

通过狄拉克的方法讨论了约束在\（S ^ 1 \）上的两个粒子的经典动力学和量子动力学。我们表明，当状态在两个子系统之间达到最大纠缠度时，测量中的色散乘积会减小。我们还对外部字段\（\ vec {B} \）的上限进行量化，以使\（\ vec {B} \ ge \ vec {B} _ {upper} \）不会降低与色散相关的乘积到一个子系统。此外，我们报告外部字段\（\ vec {B} _ {cutoff} \）的截止值，在此之上，二元纠缠消失了，复合系统的不确定性与外场之间存在直接的关系。我们注意到，在此框架中，有可能为二元系统的纠缠/非纠缠调整外部场。最后，我们证明，由于算符的隐性要求，在量子哈密顿量中产生的附加项会引起系统能量的变化。