论文标题
与旋转和反转对称性相关的一般叠加态在相空间中
General superposition states associated to the rotational and inversion symmetries in the phase space
论文作者
论文摘要
一般的量子叠加状态，包含与$ n $二维组的不可约合表示，与$ n $ n $的旋转对称性相关，即常规多边形，即环状群（$ c_n $）以及多角形的旋转和反转对象，即二峰集团（$ d_n $ d_n $）和研究。结果表明，由此产生的状态形成了$ n $维的正交状态集，这可以导致特定系统的有限表示。还建立了对称状态与重新归一化的状态之间的对应关系，这是由于从任意的，无散的初始状态中选择性擦除光子数量而产生的。例如，提出了一般的环状高斯状态。这些状态在这些状态中存在非古典特性，作为子贫民相光子统计。同样，讨论了它们在计算物理量中的使用作为两部分系统中的纠缠。
The general quantum superposition states containing the irreducible representation of the $n$-dimensional groups associated to the rotational symmetry of the $n$-sided regular polygon i.e. the cyclic group ($C_n$ ) and the rotational and inversion symmetries of the polygon, i.e. the dihedral group ($D_n$ ) are defined and studied. It is shown that the resulting states form an $n$-dimensional orthogonal set of states which can lead to the finite representation of specific systems. The correspondence between the symmetric states and the renormalized states, resulting from the selective erasure of photon numbers from an arbitrary, noninvariant initial state, is also established. As an example, the general cyclic Gaussian states are presented. The presence of nonclassical properties in these states as subpoissonian photon statistics is addressed. Also, their use in the calculation of physical quantities as the entanglement in a bipartite system is discussed.
