One-Shot Coherence Distillation: Towards Completing the Picture
One-Shot Coherence Distillation: Towards Completing the Picture
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DOI：
10.1109/tit.2019.2911102
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发表时间：
2018-08
影响因子：
2.5
通讯作者：
Qi Zhao;Yunchao Liu;Xiao Yuan;E. Chitambar;A. Winter
中科院分区：
文献类型：
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作者：
Qi Zhao;Yunchao Liu;Xiao Yuan;E. Chitambar;A. Winter
量子相干性的资源框架由 Baumgratz、Cramer 和 Plenio 引入 [Phys.莱特牧师。 113, 140401 (2014)] 并由 Winter 和 Yang 进一步发展 [Phys. 113, 140401 (2014)]莱特牧师。 116, 120404 (2016)]。我们考虑从给定资源状态的单个实例中提取纯一致性的一次性问题。具体来说，我们通过 Winter-Yang 协议的推广来确定非相干操作 (IO) 下给定保真度的可蒸馏相干性。这与最大非相干运算（MIO）和移相协变非相干运算（DIO）下的可蒸馏相干性进行了比较，后者可以被铸造为半定程序，这已由 Regula 等人之前提出。 [物理。莱特牧师。 121, 010401(2018)]。我们的结果分别以与不相干状态集的平滑最小相对熵距离和假设检验相对熵距离的变体形式给出。一次性可蒸馏相干性也与一次性随机性提取有关。此外，从 IO、MIO 和 DIO 下的一次性公式，我们可以恢复多拷贝渐进中的最佳可蒸馏率，从而产生相干性的相对熵。这些结果可以与一些当前作者之前的工作进行比较[Zhao et al., Phys.莱特牧师。 120, 070403 (2018)]关于 IO、MIO、DIO 和 SIO 下的一次性相干形成。这表明 IO、DIO 和 MIO 的可蒸馏一致性量本质上是相同的，尽管这三类操作非常不同。我们还将严格不相干运算 (SIO) 下的可蒸馏相干性与约束假设检验问题联系起来，并明确证明了渐近状态下 SIO 下的束缚相干性的存在。
The resource framework of quantum coherence was introduced by Baumgratz, Cramer, and Plenio [Phys. Rev. Lett. 113, 140401 (2014)] and further developed by Winter and Yang [Phys. Rev. Lett. 116, 120404 (2016)]. We consider the one-shot problem of distilling pure coherence from a single instance of a given resource state. Specifically, we determine the distillable coherence with a given fidelity under incoherent operations (IO) through a generalization of the Winter-Yang protocol. This is compared to the distillable coherence under maximal incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO), which can be cast as a semidefinite programme, that has been presented previously by Regula et al. [Phys. Rev. Lett. 121, 010401 (2018)]. Our results are given in terms of a smoothed min-relative entropy distance from the incoherent set of states, and a variant of the hypothesis-testing relative entropy distance, respectively. The one-shot distillable coherence is also related to one-shot randomness extraction. Moreover, from the one-shot formulas under IO, MIO, and DIO, we can recover the optimal distillable rate in the many-copy asymptotics, yielding the relative entropy of coherence. These results can be compared with previous work by some of the present authors [Zhao et al., Phys. Rev. Lett. 120, 070403 (2018)] on one-shot coherence formation under IO, MIO, DIO and also SIO. This shows that the amount of distillable coherence is essentially the same for IO, DIO, and MIO, despite the fact that the three classes of operations are very different. We also relate the distillable coherence under strictly incoherent operations (SIO) to a constrained hypothesis testing problem and explicitly show the existence of bound coherence under SIO in the asymptotic regime.