Geometric inequalities from phase space translations
Geometric inequalities from phase space translations
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DOI：
10.1063/1.4974224
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发表时间：
2017-01-01
影响因子：
1.3
通讯作者：
Vershynina, Anna
中科院分区：
文献类型：
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作者：
Huber, Stefan;Koenig, Robert;Vershynina, Anna
我们建立了一个经典的等周不等式的量子版本的Fisher信息和熵功率的量子态。关键的工具是Fisher信息不等式的状态，从一定的卷积运算的结果：后者映射的经典概率分布相空间和量子态的量子态。我们发现，这个不等式也产生了几个相关的不等式，其对应的是众所周知的经典设置：特别是，它意味着一个熵功率不等式的卷积运算以及等周不等式，并建立了熵功率沿着轨道的量子热扩散半群。作为应用，我们得到了一个Log-Sobolev不等式的量子Ornstein-Uhlenbeck半群，并认为它意味着快速收敛到一个大类的初始状态的不动点。出版社：AIP Publishing
We establish a quantum version of the classical isoperimetric inequality relating the Fisher information and the entropy power of a quantum state. The key tool is a Fisher information inequality for a state which results from a certain convolution operation: the latter maps a classical probability distribution on phase space and a quantum state to a quantum state. We show that this inequality also gives rise to several related inequalities whose counterparts are well-known in the classical setting: in particular, it implies an entropy power inequality for the mentioned convolution operation as well as the isoperimetric inequality and establishes concavity of the entropy power along trajectories of the quantum heat diffusion semigroup. As an application, we derive a Log-Sobolev inequality for the quantum Ornstein-Uhlenbeck semigroup and argue that it implies fast convergence towards the fixed point for a large class of initial states. Published by AIP Publishing.