Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings
Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings
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DOI：
10.1063/5.0066653
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发表时间：
2020-09
影响因子：
1.3
通讯作者：
M. Junge;Nicholas Laracuente
中科院分区：
文献类型：
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作者：
M. Junge;Nicholas Laracuente
微量不等式是在量子信息论中具有许多应用的通用技术，通常在非交换环境中取代经典泛函计算。然而，量子场论和全息术的物理学激发了缺乏半有限迹的 III 型冯诺依曼代数中的熵不等式。 Haagerup 和 Kosaki L p 空间能够重新表达非迹冯诺依曼代数中的迹不等式。特别是，我们从 Sutter 等人的工作中展示了广义的 Araki-Lieb-Thirring 和 Golden-Thompson 不等式。 [通讯。数学。物理。 352（1），37（2017）]。然后，使用 Haagerup 近似方法，我们证明了针对相对熵的数据处理不等式的通用恢复图修正的通用冯诺依曼代数版本。我们还展示了恢复的对数 p 保真度的次谐波。此外，我们证明相对熵的不减少等价于在两个输入状态上实现通道的 L1 等距的存在。
Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates 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 the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal 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 the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing the channel on both input states.