Recoverability for optimized quantum f-divergences
Recoverability for optimized quantum f-divergences
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DOI：
10.1088/1751-8121/ac1dc2
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
Li Gao;M. Wilde
中科院分区：
文献类型：
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作者：
Li Gao;M. Wilde
优化后的量子f-发散形成了一个包含量子相对熵和夹心Rényi相对准熵的可量化测度族。在本文中，我们建立了物理上有意义的改进的数据处理不等式的优化f-散度。特别地，该改进指出，优化的f-发散度与其通道处理版本之间的绝对差是关于当恢复通道被视为旋转的Petz恢复通道时，人们可以恢复由量子通道作用的量子态的程度的上限。这些结果不仅对三明治雷尼相对熵的数据处理不等式进行了物理上有意义的改进，而且对优化的f-发散的完全可逆性（即量子充分性）也有影响。沿着的方式，我们改进了以前的标准f-散度的数据处理不等式的物理上有意义的改进，如在Carlen和Vershynina [arXiv：1710.02409，arXiv：1710.08080]的最近工作中建立的。最后，我们将优化f-散度的定义、它的数据处理不等式以及我们所有的可恢复性结果扩展到一般的冯·诺依曼代数环境，这样我们所有的结果都可以应用于量子信息理论中最常见的有限维环境之外的物理环境。
The optimized quantum f-divergences form a family of distinguishability measures that includes the quantum relative entropy and the sandwiched Rényi relative quasi-entropy as special cases. In this paper, we establish physically meaningful refinements of the data-processing inequality for the optimized f-divergence. In particular, the refinements state that the absolute difference between the optimized f-divergence and its channel-processed version is an upper bound on how well one can recover a quantum state acted upon by a quantum channel, whenever the recovery channel is taken to be a rotated Petz recovery channel. Not only do these results lead to physically meaningful refinements of the data-processing inequality for the sandwiched Rényi relative entropy, but they also have implications for perfect reversibility (i.e. quantum sufficiency) of the optimized f-divergences. Along the way, we improve upon previous physically meaningful refinements of the data-processing inequality for the standard f-divergence, as established in recent work of Carlen and Vershynina [arXiv:1710.02409, arXiv:1710.08080]. Finally, we extend the definition of the optimized f-divergence, its data-processing inequality, and all of our recoverability results to the general von Neumann algebraic setting, so that all of our results can be employed in physical settings beyond those confined to the most common finite-dimensional setting of interest in quantum information theory.