General superposition states associated to the rotational and inversion symmetries in the phase space
英文摘要：
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.
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