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arXiv 1802.04620quant-phmath-phmath.MP
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经典图像的万花筒与量子相干态

Kaleidoscope of Classical Images and Quantum Coherent States

Oktay K Pashaev, Aygül Koçak

摘要:

从Glauber相干态构造的用于描述量子比特的薛定谔猫态被推广到与正n多边形对称性和单位根有关的万花筒相干态。这个量子万花筒的动机是我们的方法的经典流体力学图像在楔形域,描述了$q$ -微积分的解析函数与$q$作为一个原始的根的单位。详细描述了三重态和四重态的情况。这些状态的归一化公式需要引入具有mod 3和mod 4对称性的指数函数的特定组合。我们证明了这些态可以通过量子傅里叶变换为任意的$n$生成,并且可以提供量子数、量子数和一般的量子数单位的量子信息。讨论了我们的态与量子群和量子演算的关系。

英文摘要:

The Schrödinger cat states, constructed from Glauber coherent states and applied for description of qubits are generalized to the kaleidoscope of coherent states, related with regular n-polygon symmetry and the roots of unity. This quantum kaleidoscope is motivated by our method of classical hydrodynamics images in a wedge domain, described by $q$-calculus of analytic functions with $q$ as a primitive root of unity. The cases of the trinity states and the quartet states are described in details. Normalization formula for these states requires introduction of specific combinations of exponential functions with mod 3 and mod 4 symmetry. We show that these states can be generated for an arbitrary $n$ by the Quantum Fourier transform and can provide qutrits, ququats and in general, qudit units of quantum information. Relations of our states with quantum groups and quantum calculus are discussed.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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