论文标题
多元轨迹不平等，pfidelities和tracial设置超出的通用恢复
Multivariate Trace Inequalities, p-Fidelity, and Universal Recovery Beyond Tracial Settings
论文作者
论文摘要
痕量不平等是量子信息理论中许多应用的一般技术，通常会在非交通设置中取代经典的功能演算。然而，量子场理论和全息图的物理学激发了缺乏半蛋白能痕迹的III型von Neumann代数的熵不平等。 Haagerup和Kosaki $ L_P $空间在非领域的von Neumann代数中启用了重新表达的痕量不平等。特别是，我们为广义的Araki-lieb-thirring和Golden-Thompson不平等现象（Sutter，Berta \＆Tomamichel 2017）展示了这一点。然后，使用Haagerup近似方法，我们证明了一般的von Neumann代数版本的Univeral Recovery MAP校正相对熵的数据处理不等式。我们还显示了对数恢复的对数PFIDELITY的次谐度。此外，我们证明，相对熵的不递减等效于存在在两个输入状态下实现通道的$ l_1 $ ismemetry。
Trace inequalities are general techniques with many applications in quantum information theory, often replacing classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivate entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki $L_p$ spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki-Lieb-Thirring and Golden-Thompson inequalities from (Sutter, Berta \& Tomamichel 2017). Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of univeral recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that non-decrease of relative entropy is equivalent to existence of an $L_1$-isometry implementing the channel on both input states.
