发表机构
University of Bucharest（布加勒斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出用所有正则相干态的紧框架替代厄米-高斯基来描述高斯态，得到混合高斯态框架依赖相干性的显式公式，并构造快速收敛的离散变量量子态序列。
AI 中文摘要
希尔伯特空间通常使用正交基来描述，但也可以使用紧框架来定义更一般的描述。在连续变量高斯态的情况下，相干性通常使用厄米-高斯基来描述。我们提出了一种使用所有正则相干态的紧框架的替代描述。用相干态描述高斯态比用厄米-高斯基更简单，这使我们能够获得一个显式公式，将混合高斯态的框架依赖相干性描述为协方差矩阵的行列式和迹的函数。对于每个混合高斯态，我们构造了一个离散变量量子态序列，当希尔伯特空间的维度变得足够大（15或更大）时，该序列（就纯度和相干性而言）快速收敛到该混合高斯态。在离散情况下，相干性是相对于所有离散相干态的紧框架来测量的。
英文摘要
A Hilbert space is usually described using an orthonormal basis, but a more general description can be defined using a tight frame. In the case of continuous-variable Gaussian states, the coherence is usually described using the Hermite-Gauss basis. We present an alternative description using the tight frame of all canonical coherent states. The description of Gaussian states in terms of coherent states is simpler than in terms of Hermite-Gauss basis, and this allows us to obtain an explicit formula describing the frame-dependent coherence of a mixed Gaussian state as a function of the determinant and the trace of covariance matrix. For each mixed Gaussian state, we construct a sequence of discrete-variable quantum states rapidly convergent to it (as concern the purity and coherence) when the dimension of Hilbert space becomes large enough (15 or more). In the discrete case, the coherence is measured with respect to the tight frame of all discrete coherent states.
Comments10 pages, 1 figure. More details are available on my homepage https://unibuc.ro/user/nicolae.cotfas/
