标题： 非高斯态的非广播性 显示英文标题

标题： No-broadcasting of non-Gaussian states

摘要： 高斯态在连续变量量子系统的物理中具有基础重要性。它们因其易于实验制备而受到青睐，并且具有简洁而优雅的数学描述。然而，许多提出的量子技术要求我们超越高斯态的范围，引入非高斯元素。在量子资源理论的框架下，我们可以将非高斯态视为资源，而高斯操作和态视为自由资源，可以轻松使用和制备。在这样的资源理论结构下，广播资源的任务是确定状态的资源内容是否可以以有意义的方式克隆，如果可能的话，这将提供一种强大的资源操作手段。在这项工作中，我们证明通过高斯操作无法广播非高斯态。为此，我们首先表明非高斯性的相对熵不是超可加的，这使其排除在对这类不可能结果的分析之外。我们的证明基于对高斯操作固定点的理解，并与控制系统理论相关。该不可能定理还指出，如果两个最初不相关的系统通过高斯动力学相互作用，并且在一个子系统中产生了非高斯性，则另一个子系统的非高斯性必须减少。此外，在保持自由操作集为高斯操作的情况下，我们还可以对Wigner负性和真实量子非高斯性的广播进行评论。 显示英文摘要

摘要： Gaussian states are of fundamental importance in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and an elegant mathematical description. Nevertheless, many proposed quantum technologies require us to go beyond the realm of Gaussian states and introduce non-Gaussian elements. In terms of quantum resource theory, we can then recognize non-Gaussian states as resources and Gaussian operations and states as free, which can be used and prepared easily. Given such a structure of resource theory, the task of broadcasting the resource is to determine if the resource content of a state can be cloned in a meaningful way, which, if possible, provides a strong operation for manipulation of the resource. In this work, we prove that broadcasting of non-Gaussian states via Gaussian operations is not possible. For this, we first show that the relative entropy of non- Gaussianity is not super-additive, which rules it out as a prime candidate in the analysis of such no-go results. Our proof is then based on understanding fixed points of Gaussian operations and relates to the theory of control systems. The no-go theorem also states that if two initially uncorrelated systems interact by Gaussian dynamics and non-Gaussianity is created at one subsystem, then the non-Gaussianity of the other subsystem must be reduced. Further, keeping the set of free operations fixed to Gaussian operations, we can also comment on the broadcasting of Wigner negativity and genuine quantum non-Gaussianity.